Masking-based b -order MMSE speech enhancement
Chang Huai You
a,b,*
,Soo Ngee Koh b ,Susanto Rahardja
a,b
a
Division of Media,Institute for Infocomm Research,21Heng Mui Keng Terrace,Singapore 119613,Singapore
b
School of Electrical and Electronic Engineering,Nanyang Technological University,50Nanyang Avenue,Singapore 639798,Singapore
Received 8September 2004;received in revised form 21April 2005;accepted 24May 2005
Abstract
This paper considers an e?ective approach for attenuating acoustic noise and mitigating its e?ect in a speech signal.In this approach,
human perceptual auditory masking e?ect is incorporated into an adaptive b -order minimum mean-square error (MMSE)speech enhancement algorithm.The relationship between the value of b and the noise-masking threshold is introduced and analyzed.The algorithm is based on a criterion by which the inaudible noise may be masked rather than suppressed.It thereby reduces the chance of distortion introduced to speech due to the enhancement pro-cess.In order to obtain an optimal estimation of the masking threshold,a modi?ed way to measure the relative thresh-old o?set is described.The performance of the proposed masking-based b -order MMSE method has been evaluated through objective speech distortion measurement,spectrogram inspection and subjective listening tests.It is shown that the proposed method can achieve a more signi?cant noise reduction and a better spectral estimation over the conven-tional adaptive b -order MMSE method and the conventional over subtraction noise-masking method.ó2005Elsevier B.V.All rights reserved.
Keywords:Speech enhancement;Minimum mean-square error (MMSE);Masking properties
1.Introduction
Weak speech signals such as nasals,fricatives and a?ricates are often seriously contaminated
by noise,resulting in reduction of speech intelligi-bility.So far,speech enhancement research mainly aims to solve the problem in which the speech sig-nal is degraded by uncorrelated additive noise and only the noisy speech signal is available.Many ap-proaches in the time/frequency domain have been investigated to date.In terms of the methodology adopted,the most popular methods for speech enhancement can be broadly categorized as (i)spectral amplitude estimation such as Wiener ?ltering (Lim and Opppenheim,1979),spectral
0167-6393/$-see front matter ó2005Elsevier B.V.All rights reserved.doi:10.1016/j.specom.2005.05.012
*
Corresponding author.Address:Division of Media,Insti-tute for Infocomm Research,21Heng Mui Keng Terrace,Singapore 119613,Singapore.Tel.:+6568748534.
E-mail addresses:echyou@https://www.doczj.com/doc/283510455.html,.sg (C.H.You),esnkoh@https://www.doczj.com/doc/283510455.html,.sg (S.N.Koh),rsusanto@https://www.doczj.com/doc/283510455.html,.sg (S.Rahardja).
Speech Communication 48(2006)57–70
subtraction(McAulay and Malpass,1980), Ephraim and Malah(E-M)MMSE(Ephraim and Malah,1984)and log spectral amplitude (LSA)estimation(Ephraim and Malah,1985); (ii)speech production model-based method (Gannot et al.,1998);(iii)hearing perceptual crite-ria-based enhancement(Virag,1999;You et al., 2004b;Hansen and Nandkumar,1995;Tsoukalas et al.,1997);(iv)text-directed non-real-time speech enhancement(Hansen and Pellom,1997); (v)hidden Markov model(HMM)method (Ephraim et al.,1989);and(vi)eigen decomposition subspace method(Ephraim and Van Trees,1995).
One of the main approaches of speech enhance-ment algorithms is to obtain the best possible esti-mate of the short time spectral amplitude(STSA) of a speech signal from a given noisy speech.Most of the STSA estimators ignore the estimation of the phase of a speech signal as it has been well demonstrated that the human ear is insensitive to the phase of the speech signal(Lim and Wang, 1982;Vary,1985).There are many existing speech enhancement methods which exploit the properties of the human auditory system.The main aim of these methods is to?nd an optimal trade-o?between noise suppression,speech distortion and residual tonal noise level(Virag,1999;Hansen and Nandkumar,1995;Tsoukalas et al.,1993). In addition,most of them use the a posteriori SNR to achieve noise suppression.It is assumed that human listeners are unable to perceive an additive noise so long as it remains below the masking threshold.In(Virag,1999;Tsoukalas et al.,1997),Masking properties are incorporated into generalized spectral subtraction,which can be expressed as^S k??j X k j bàE fj N k j b g 1=b for some constant b,where k is the frequency bin index, S k,X k and N k are Fourier transforms of a win-dowed segment of speech,noisy speech and noise, respectively.In essence,the generalized spectral subtraction method hinges on the estimation of the value of a spectral amplitude/power term based on its expected value.For examples,when b=1,it is an amplitude spectral subtraction which directly uses E{j N k j}to replace j N k j;when b=2,it is a power spectral subtraction which not only di-rectly uses E{j N k j2}to replace j N k j2,but also uses
E f S k N?
k g and E f N k S?
k
g to replace S k N?
k
and N k S?
k
.
The expectations of S k N?
k
and N k S?
k
are equal to
zero due to the statistical independence and zero
mean assumptions(Lim and Opppenheim,1979,
p.11),where N?
k
and S?
k
represent complex conju-
gates of N k and S k.For the b=2case,it is also
equivalent to estimating the square root of the
maximum likelihood estimator of each signal
spectral component variance based on a complex
Gaussian model(McAulay and Malpass,1980,p.
138).Consequently,optimal estimation of a
speech signal cannot be obtained using the mathe-
matical model of generalized spectral subtraction
method,which does not lead to improvement in
the intelligibility of the processed speech(Lim,
1978).Therefore,the generalized spectral subtrac-
tion approach may be useful for those applications
where perception of noise reduction,without any
signi?cant drop in speech intelligibility,is desired
(Lim,1978,p.472).The presence of obvious and
annoying musical tones in the processed speech
caused by the imperfect model of generalized spec-
tral subtraction is yet another of its drawbacks.
In contrast to many masking-based speech
enhancement methods which are based on general-
ized spectral subtraction,we propose an enhance-
ment method to incorporate the masking
properties into b-order MMSE.The b-order
MMSE speech enhancement method(You et al.,
2003,2005)is an optimal estimation method.It
is derived by minimizing the mean-square error
cost function J?E feA b
k
à^A b
k
T2g based on the com-
plex Gaussian distribution model and statistical
independence assumption.Herein,A k and^A k are
respectively the original and the estimated spectral
amplitude of the speech signal at frequency bin k.
E-M MMSE and E-M LSA can be seen as special
cases of b-order MMSE,which correspond to the
case when b equals to one and b approaches zero
respectively.In(Cappe′,1994),the elimination of
musical noise phenomenon of the E-M MMSE
method is analyzed;it shows that the E-M MMSE
noise suppressor is e?ective if a nonlinear smooth-
ing procedure is used to obtain more consistent
estimates of the a priori and a posteriori SNRs
which are used to control the gain function.Obvi-
ously,the principle of musical noise elimination in
(Cappe′,1994)can also be applied to adaptive b-
order MMSE(You et al.,2005).
58 C.H.You et al./Speech Communication48(2006)57–70
In this paper,b-order MMSE is modi?ed so as to incorporate the noise-masking threshold(You et al.,2004a).Speci?cally,the value of b is made to vary according to the frame SNR and masking threshold.Simulation results indicate that the masking-based b-order MMSE estimator outper-forms many existing spectral suppression methods in terms of both objective and subjective measures. The remainder of this paper is organized as follows.The masking-based b-order MMSE speech enhancement method is introduced in Section2.The performance of the masking-based b-order MMSE estimation is investigated in Section3.Section4gives the conclusion.
2.Masking-based b-order MMSE speech enhancement
Human auditory modelling has been widely used in acoustic signal processing,especially in audio and speech coding.This model is based on the masking phenomenon and related to the concept of critical band analysis,which is a central analysis mechanism of the inner ear.The masking properties are modelled by the noise-masking threshold.Masking is present because the auditory system is incapable of distinguishing two signals which are close to one another in spectral spacing. Masking e?ects occur not only when sounds are presented simultaneously,but also when they are not.There are two non-simultaneous masking—pre-masking and post-masking.Pre-masking takes place during the period of time before the masker is present,while post-masking follows simulta-neous masking.Noise masking is a well-known psychoacoustic property of the human auditory system that has already been applied with suc-cess to speech and audio coding in order to par-tially or totally mask distortions introduced in the coding process.In this paper,we only con-sider frequency domain masking,or simultaneous masking,i.e.,a weak signal is made inaudible by a strong signal occurring simultaneously.This phenomenon is modelled via a noise-masking threshold,below which all spectral components are inaudible.The masking-based speech enhance-ment approach basically incorporates the noise-masking properties into a speech enhancement algorithm.
2.1.Gain of a masking-based b-order MMSE speech enhancement
An observed noisy speech signal x(t)is assumed to be a clean speech signal s(t)degraded by uncor-related additive noise n(t),i.e.,
xetT?setTtnetT;06t6T.e1TLet S k=A k e j a k,N k,and X k=R k e j#k denote the k th spectral component of the clean speech signal s(t),noise n(t),and the observed noisy speech x(t),respectively,in the analysis interval[0,T]. The gain function of the b-order MMSE(You et al.,2003,2005)is expressed by
Gen k;c
k
;bT?
????t
k
p
c k
C
b
2
t1
Mà
b
2
;1;àt k
!1=b
;
e2T
where C b
2
t1
àá
is the gamma function and Màb
2
;1;àt k
àá
is the con?uent hypergeometric function(Ephraim and Malah,1984;You et al., 2005).t k is de?ned as
t k?
n k
1tn k
c k;e3Tn k an
d c k represent th
e a priori SNR and a poste-riori SNR respectively(Ephraim and Malah, 1984),i.e.,
n k?
g sekT
g nekT
;c
k
?
R2
k
g nekT
;e4T
where g n(k)=E[j N k j2]and g s(k)=E[j S k j2]are the variances of the k th spectral components of noise and the speech signal,respectively.The a priori SNR,n k,can be estimated by the decision-directed approach(Ephraim and Malah,1984)as follows: ^n
k
elT?e1àaTmax?c kelTà1;0
ta
j Ge^n kelà1T;c kelà1T;bTX kelà1Tj2
g nekT
;
e5Twhere l denotes the index of frame.Normally,the parameter a is set to0.98(Ephraim and Malah, 1984;Cappe′,1994).
C.H.You et al./Speech Communication48(2006)57–7059
With masking-based speech enhancement,the amount of noise to be reduced is set at the level of noise that can be masked by the clean speech in order to reduce the distortion introduced to speech due to the enhancement process.Subse-quently,the amount of noise reduction obtained by using a masking-based enhancer during speech activity period may be more than that obtained by using the same enhancer without masking consid-eration.
On the other hand,the amount of noise reduction is not a?ected during speech
pause
peri-od.In order to avoid a sudden change from speech activity to speech pause in the perceptual sense,a spectral ?ooring is adopted.We therefore modify the gain function as follows:
T
where q 1(k )is a threshold factor.Together with
q 2(k ),it determines the lowest SNR limitation below which a spectral ?oor gain function is applied in place of b -order MMSE gain.q 2(k )is a coe?cient of spectral ?oor which is a?ected by the masking threshold and its minimum and max-imum settings.In the case of speech pause period,as the masking threshold is equal to the absolute masking threshold value which is too low to be considered,q 2(k )is therefore determined by its minimum setting.Through a large number of simulations,we propose that the two parameters be made directly proportional to the masking threshold with the set of minimum and maximum 1T
T
and T min (l )are the maximum and minimum values of noise-masking threshold T f (l ,k )at current frame l .As mentioned in (Virag,1999),the spec-tral ?ooring leads a reduction of residual noise and an increased level of background noise.The estimate of speech signal therefore is given by ^S
k ?G M en k ;c k ;b TX k .e9T
2.2.Modi?ed relative threshold o?set and masking threshold
The noise-masking threshold is obtained through modelling the frequency selectivity of the human auditory system and its masking proper-ties.The estimation of noise-masking threshold in-cludes the preliminary estimation of the speech,2critical band analysis,spreading function,the rela-tive threshold o?set,the masking threshold nor-malization and the absolute auditory threshold comparison (Johnston,1988).
There are two ways to obtain the relative threshold o?set.One is given by a simple estima-tion which is based on the fact that the speech signal has a tone-like nature in the lower critical bands and a noise-like nature in the higher bands (Virag,1999).It can be represented using a ?xed relative threshold o?set,O f (k ),shown in Fig.1(Virag,1999).It is also observed that the ?xed rel-ative threshold o?set,O f (k ),is generally suitable for most clean speech segments.Another is based on an estimation of the tonality in a particular crit-ical Bark band,and the corresponding relative threshold o?set is then obtained.The noise-mask-ing threshold calculation considers noise-masking tone and tone-masking noise (Hellman,1972;
1
In (Virag,1999),combining with the generalized spectral subtraction algorithm,they are reciprocally proportional to the masking threshold with a di?erent set of maximum and minimum values.
2
We use b -order MMSE method with b being a certain ?xed value.In our simulation,we set b to 0.5.In (You et al.,2004a ),we obtained the preliminary speech estimate by using spectral subtraction.
60 C.H.You et al./Speech Communication 48(2006)57–70
Schroeder et al.,1979).The noise-masking tone is estimated as (14.5+k )dB below the spread criti-cal spectrum,C (k )(in dB),where k is the Bark frequency.The tone-masking noise is estimated to be 5.5dB below C (k )uniformly across the spread critical spectrum.In order to apply the properties of the noise-masking tone and the tone-masking noise,
the spectral ?atness mea-sure (SFM)(Hellman,1972)is used to determine if the signal is close to noise or tone.SFM is de?ned by the ratio of the geometric mean (G m )to the arithmetic mean (A m )of the power spectral density components (P (j ))in each critical band,i.e.,SFM dB ek T?10log 10
G m ek T
A m ek T
;k ?1;2;...;B k ;
e10T
G m ek T?
Y M ek Tj ?1
eP ej TT
1M ek T
;
A m ek T?
P M ek T
j ?1
P ej T
M ek T
;
e11T
where B k is the number of critical bands and M (k )denotes the number of frequency bins in each band k .A coe?cient of tonality,a (k ),is de?ned as
a ek T?max min SFM dB ek T
SFM dB max ;1 !;0&'
.e12T
Here SFM dBmax is set to à60dB.SFM dB of à60dB represents a pure tone-like signal,and SFM dB of 0dB indicates a completely noise-like signal.The variable relative threshold o?set,O a (k ),in each critical band is given by
O a ek T?a ek Te14.5tk Tt?1àa ek T 5.5.e13T
Since we only have the noisy speech signal,the pre-liminary estimate of the speech signal is usually
not very accurate.Consequently,the estimation of the variable relative threshold o?set is also a?ected.This is because the residual noise of the preliminary estimated speech may severely change the original tonality of the speech signal.As a re-sult of the inaccurate relative threshold o?set,the estimation error of the masking threshold in-creases.In (Virag,1999),the ?xed relative thresh-old o?set is exploited and compensated with a slight modi?cation by taking into account the tone-like nature of the musical residual noise for k >15.Herein,we propose a modi?ed o?set by merging both the ?xed and variable o?sets to achieve a more e?ective application of the masking properties.The modi?ed relative threshold o?set,O m (k ),is given by
O m ek T?a a O a ek Tte1àa a TO f ek T;
e14T
where a a is a weighting constant set to https://www.doczj.com/doc/283510455.html,paring with the relative threshold o?set scheme in (Virag,1999)and the pure variable relative threshold o?set,simulation study shows that the modi?ed relative threshold o?set leads to a slight improvement in our speech enhancement approach in terms of both segmental SNR and Itakura-Saito measures.
With the above mentioned modi?ed relative threshold o?set,we compute the masking thresh-old.Fig.2gives the ?ow chart of the computation of masking threshold,T (l ,k ).
2.3.Adaptation of b value based on masking properties
According to Cappe
′?s work (1994)on E-M MMSE,when the speech level is well above the noise level,the a priori SNR estimation equation involves a mere one-frame delay of instantaneous SNR;when the speech signal level is close to or be-low the noise level,the a priori SNR estimation equation has a smoothing e?ect.Consequently,we can reasonably assume n k =c k à1as a mean-ingful possible path for tracking the gain changes when we discuss di?erent estimators.As shown
C.H.You et al./Speech Communication 48(2006)57–70
61
in Fig.3,we can see that Wiener ?ltering may over-attenuate the weak signals (low SNR),E-M LSA (similar to b =0.001case)performs better in preserving the weak signals,and b -order MMSE has obviously a much wider range of gain values and thus more ?exible and e?ective for estimating weak spectral components provided that the b value can be made to appropriately adapt to di?erent signal component strengths.The over-attenuation of weak spectral components (i.e.,low SNR)in the case of Wiener ?ltering can be ob-served clearly through inspection of spectrograms
obtained from a large number of simulations using many di?erent speech utterances corrupted by dif-ferent types of noise.
Since the estimate of speech signal spectral amplitude A k given x (t )(06t 6T )is based on modelling speech and noise spectral components as statistically independent Gaussian random vari-ables,which is well elaborated in (Ephraim and Malah,1984,pp.1109–1110).The statistical inde-pendence assumption in the Gaussian model is equivalent to the assumption that the Fourier
expansion
coe?cients
are uncorrelated.As a conse-quence,we have ^A k ?????????????????????????????????????????????E f A b k j x et T;06t 6T g b q ?????????????????????????????????????????????
E f A b k j X 1;X 2;...;X K g b
q to be equivalent to ????????????????????E f A b k j X k g b
q ,where K denotes the number of fre-quency bins.Therefore the k th spectral gain of Eq.(2)is only a function of a priori and a posteri-ori SNRs of the k th frequency bin rather than the SNRs of other frequency bins.Though the statisti-cal independence assumption is reasonably valid and useful for estimating the amplitude in a certain frequency bin,the interactive contribution for the estimation of the amplitude from other frequencies
may be helpful.In particular,for estimation of ^A
k ,the value of b is designed to adapt to the frame SNR,and it also have been found to be e?ective (You et al.,2003).The de?nition of frame SNR is given as follows:
e15TIn the enhancement processing,as we only have
the observed noisy speech signal,and we do not have the clean speech signal and noise signal,the frame SNR can be approximated by using the following equation:
e16TAccording to You et al.(2003,2005),it is desir-able for b to increase in value as N (l )increases,and to decrease in value when N (l )decreases.
The maximum allowable noise spectrum (or distortion spectrum)which is not discernible by a human listener is called the noise-masking
62 C.H.You et al./Speech Communication 48(2006)57–70
threshold.It is well known that some audio spec-tral components are inaudible to human listeners when they are under the masking threshold of other components(Virag,1999;Tsoukalas et al., 1997;Johnston,1988;Hellman,1972;Schroeder et al.,1979).Though a speech signal with some inaudible components has almost the same percep-tual quality as the one without the inaudible com-ponents to human listeners,it may have di?erent e?ects when it is input to a speech recognition system where some weak spectral components, though inaudible,may be critical to the successful recognition of some phonemes.The results re-ported in(Virag,1999)substantially con?rm this https://www.doczj.com/doc/283510455.html,ing noise-masking threshold as weighting factor but not as a threshold has been applied to speech enhancement(Virag,1999).We can use auditory masking e?ects to achieve the classic trade-o?between noise reduction and speech distortion,wherein the inaudible noise spectral components together with the correspond-ing speech spectral components are not attenu-ated,and thereby reducing the chance of further distortion to speech.On the other hand,those noise spectral components that are audible must be removed(Tsoukalas et al.,1997).
We propose to make the b value such that it not only depends on the frame SNR which represents the power of the speech signal in the current frame but also relies on the noise-masking threshold in a particular Bark band,in order to achieve an opti-mal trade-o?between noise reduction and speech distortion.As a result,b is made to be a function of frame SNR and the masking threshold.We assume the function could be expressed as a poly-nomial of the two variables as follows:
bel;kT?
X1
i?0X1
j?0
c ij NelTi H fel;kTj
?s0ts1NelTts2H fel;kT
ts3NelTH fel;kTtUeO hT;e17Twhere H f represents the perceptual factor(to be discussed later in the paper)of the human auditory system in the frequency domain,c ij and s i (i,j=0,1,2,...,1)denote the polynomial coe?-cients,and U(O h)represents the high-order polynomial terms.By ignoring the high-order polynomial terms and assuming b is a monotonic non-decreasing function of N(l),we can express b(l,k)approximately in the following form:
^bel;kT?s
ts1NelTts2H fel;kT
ts3max?NelTàs4;0 H fel;kT.e18TFrom Eq.(18),we can see the parameters s i(i=0, 1,...,4)determine the e?ectiveness of the b-order MMSE speech enhancement system.Actually,s0 is a?oor that determines the general level of b va-lue,and s1and s2decide the extent the frame SNR and the masking threshold in?uence the suppres-sion gain value.s3adds another contribution that is based on both the frame SNR and noise-mask-ing threshold,while s4is to give a lower bound contribution to gain function from frame SNR. It means frame SNRs below s4will not a?ect the gain value.
Through a large number of computer simula-tion experiments using real speech and noise data, the s i(i=0,1,2,...)parameters are appropriately adjusted.Here,we give the empirically obtained polynomial coe?cients of Eq.(18)as follows:
^bel;kT?0.942t0.121NelTt0.981H
f
el;kT
t0.187max?NelTt6.7;0 H fel;kT.e19TIn contrast to the conventional optimal estimation approach based on a cost function and using mathematical derivation,Eq.(19)is an empirical formula with parameters(s i)obtained from simu-lation experiments.As will be shown in Section 3,good simulation results are obtained by using these parameter values.Further justi?cations for Eq.(19)are given in the following paragraph.
In our proposed b-order MMSE-based speech enhancement,a higher masking threshold will result in a higher b value and consequently a high-er gain in the estimation process.This will ensure that some speech spectral components would not be over-attenuated and thus minimizes distortions to the speech signal.Based on the noise-masking threshold,we can determine the power and spectral shape of noise that might be inaudibly in-serted into the speech signal.Consequently,the frequency-dependent masking threshold can be
C.H.You et al./Speech Communication48(2006)57–7063
64 C.H.You et al./Speech Communication48(2006)57–70
regarded as the reference spectrum for re-shaping the noise.If the masking threshold is high,residual noise will mostly be masked and become inaudible.Hence,there is no need to attenuate it in order not to increase the level of distortion to speech.In this
case,the b value should be high
which results in a relatively high gain value for weak spectral compo-nents.However,if the masking threshold is low,residual noise will be annoying to human listeners and it has to be reduced in amplitude.This is done by reducing the b value appropriately.In short,we should use high b value for components with high SNR values,and also when the masking threshold is high.
In addition to adapting b based on frame SNR and masking threshold and using Eq.(19),we also limit b to a maximum value of 4as too high a b value will leave most of the noise components intact.The ?nal b value is therefore given by ~b
el ;k T?min f max f ^b el ;k T;0.001g ;4g .e20T
The perceptual factor H is obtained by the follow-ing normalization step:e21T
The frequency domain perceptual factor H f has its corresponding expression H in the Bark domain,i.e.,H f (l ,k )=H (l ,k ).
Fig.4gives an example of the value of b adap-tation by using Eq.(19)for a speech utterance con-taminated by F-16cockpit noise with an input
segmental SNR of à10dB.
2.4.Implementation of masking-based speech enhancement method
In this section,we describe the implementation of the proposed masking-based speech enhance-ment system.As shown in Fig.5,a noisy speech signal is Hanning windowed and then transformed into the spectral domain.The estimate of noise spectral amplitude is obtained during speech pause period.Following the pre-estimation of speech spectral amplitude by using ?xed-order MMSE method,the masking threshold is computed.With the noisy speech spectral amplitude and the esti-mate of noise,the frame SNR is provided.Conse-quently,the value of b is calculated according to the masking threshold and the frame SNR.Final-ly,the enhancement processing is done by using the masking-based b -order MMSE gain function with the adapted b value.
The elimination of musical tones using the E-M STSA-MMSE (Ephraim and Malah,1984)estima-tor is described in (Cappe
′,1994).It is mainly due to the e?ectiveness of the so called ?decision-direc-ted approach ?for estimating the a priori SNR,n k .
C.H.You et al./Speech Communication 48(2006)57–7065
Obviously,this musical tone elimination feature can also be applied to the b-order MMSE described by Eq.(2)for any value of b.
3.Performance evaluation
To evaluate the performance of the proposed masking-based b-order MMSE speech enhance-ment method,?ve di?erent types of noise taken from the NOISEX-92database(Varga and Steene-ken,1993)are used in our simulation experiments. They are white Gaussian noise,interior Volvo car noise,F16cockpit noise,Babble noise(100people speaking in a canteen)and Leopard(military vehi-cle)noise.A total of30phonetically balanced speech utterances from the TIMIT database (Garofolo,1988)are used in our evaluation.Fif-teen of the utterances are produced by male speak-ers and another?fteen by female speakers.The test utterances are sampled at8kHz and the frame size used is256samples(32ms)in length.The samples are Hamming windowed with50%overlap between adjacent frames.In order to simplify the noise estimation,we use minimum statistics (Martin,1994)and choose noise compensation factor3about 1.5$2.3for di?erent speech estimators.For Eqs.(7)and(8),we empirically select q1min=1,q1max=6.28,p2min=0and p2max=0.015.
As it is well known that segmental SNR (seg.SNR)(Quackenbush et al.,1988)is more accurate in indicating the speech distortion than the global SNR,noise was therefore added at dif-ferent input seg.SNRs for each of utterances in our simulation.The segmental SNR is measured by computing the SNR for each of the speech frames and averaging these SNRs over the entire utter-ance.It is de?ned as
N seg?1
L s
X L sà1
l?0
N frameelT;e22T
where N frame(l)is the frame SNR which is de?ned as N frameelT?10log10
P M sà1
j?0
s2eM s làjT
P M sà1
j?0
?^seM s làjTàseM s làjT 2
!
;
e23Ts denotes a clean speech signal,and^s denotes the noisy speech or enhanced speech.M s denotes the number of samples per frame and L s is the number of frames.M s is set to128for8kHz sampling rate.
Adding noise at a desired input segmental SNR level for a noisy utterance can be done by comput-ing an initial seg.SNR,SNR I(in dB),with the corresponding initial multiplication factor P I, where x I(t)=s(t)+P I n(t).The noisy speech utter-ance at a desired input seg.SNR can then be
3The factor is used to compensate the bias of the minimum
estimate(Martin,1994).
66 C.H.You et al./Speech Communication48(2006)57–70
obtained by x d(t)=s(t)+P d n(t),where P d?P I10eSNR IàSNR dT=20.
The speech enhancement algorithms for evalua-tion comparisons include Wiener?ltering(Lim and Opppenheim,1979,p.13),over-subtraction masking(Virag,1999),E-M LSA(Ephraim and Malah,1985),E-M MMSE(Ephraim and Malah, 1984),the adaptive b-order method(You et al., 2003)and the proposed masking-based adaptive b-order MMSE method.Figs.6–8show the seg.SNR,average PESQ and Itakura-Saito(IS) distortion(Quackenbush et al.,1988)measure,4respectively,of the enhanced speech processed by the di?erent enhancement methods,for di?erent input seg.SNRs(à10dB,à5dB,0dB,5dB and 10dB),with white noise in(a),as well as F16cock-pit noise in(b).Fig.9shows the spectrograms of the original clean speech,the input noisy speech and the enhanced speech obtained by the various enhancement methods.From the obtained results, it is apparent that our proposed method almost al-ways has the best seg.SNR,PESQ and IS distor-tion measure as well as spectrogram inspection as compared to other methods.
It is well accepted that meaningful de?nition of speech quality must be based on human percep-tion.Speech signals can be compared and
4The highest15%of the IS distortion values were discarded,
to exclude unrealistically high spectral distortion values.
C.H.You et al./Speech Communication48(2006)57–7067
evaluated in terms of intelligibility,naturalness,and suitability for a particular application.The Mean Opinion Score (MOS)is one of the most popular and widely accepted subjective measures of ‘‘acceptability’’that is in?uenced by the intelli-gibility and quality of the utterances being
evalu-
Fig.9.Speech spectrograms (male:‘‘The ?fth jar contains big,juicy peaches’’,8kHz sampling rate):(a)clean speech;(b)noisy speech (F16noise);(c)Wiener ?ltering method;(d)Over-subtraction masking method;(e)E-M LSA;(f)E-M MMSE;(g)adaptive b -order MMSE;(h)proposed masking-based adaptive b -order MMSE.
68 C.H.You et al./Speech Communication 48(2006)57–70
ated.Forty listeners including15researchers,15 non-researchers and10students were invited to as-sess the subjective quality.Before a listening test, the listeners are explained the criterion of marking the score for quality of the speech utterances by using the MOS score table(Quackenbush et al., 1988).Two speech sentences with one from a female speaker and the other from a male speaker contaminated by F16noise at input seg.SNR of à5dB are processed by di?erent enhancement methods.Listeners are required to listen three times for each of the speech signals including noisy and enhanced ones.For each of utterances,the lis-tening order of the enhanced speech signals en-hanced by various enhancement methods is unknown to the listeners.Table1gives the MOS listening test results which con?rm that our proposed masking-based enhancement method has the best performance for human listeners as compared to other enhancement methods.
To implement the adaptive b-order MMSE algorithm for real-time realization,the computa-tional complexity involved in Eq.(2)can be simpli-?ed(You et al.,2005).On the other hand,from the view point of processing complexity,the additional step of computing the masking threshold does not add too demanding a cost because our algorithm is working in the spectral domain using FFT.
4.Conclusion
The focus of our study is to develop an opti-mal speech enhancement algorithm that would maximize noise reduction while minimizing speech distortion.In this paper,we propose an adaptive b-order STSA-MMSE speech enhance-ment method which incorporates the perceptual properties of the human auditory system.The pro-posed method leads to an improvement in perfor-mance over the conventional adaptive b-order MMSE method.The improvement is achieved due to the e?ectiveness of adapting the b value accord-ing to the frame SNR and the masking threshold. In addition,we propose a modi?ed relative thresh-old o?set measure to provide more appropriate information which is useful in forming the masking properties measure.
Through computer simulations,our proposed algorithm has been shown to outperform many other speech enhancement methods and has a good trade-o?for minimizing both speech distor-tion and residual noise level,especially for the case of weak spectral components of speech signal cor-rupted by noise.This conclusion is supported by visual spectrogram inspection,segmental SNR measure,PESQ,Itakura-Saito measure,as well as MOS listening tests.
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Table1
MOS values for the following methods:(1)WF:Wiener
?ltering;(2)LSA:E-M log spectral amplitude;(3)MMSE:
E-M MMSE;(4)OM:over-subtraction based on masking
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Methods
WF LSA MMSE OM b Màb
MOS 2.01 3.25 2.98 2.81 3.39 3.52
The input seg.SNR isà5dB with MOS=1.85.
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70 C.H.You et al./Speech Communication48(2006)57–70
【第一梯队学校评价标准】 1. 独特的教学和教育理念; 2.独树一帜的教育方法或深厚的办学积淀; 3.足够高的社会美誉度，并受到市级乃至国家级的表彰; 4.一流的软硬件; 5.较好的对口初中等。 【第二梯队学校评价标准】 1. 优异且稳定的升学成绩(或有推优); 2.区内突出的教学特色; 3.足够的师资力量; 4.发展劲头明显或受到市、区级相关单位的重点关注等。 【第三梯队学校评价标准】 1.潜力巨大的新学校或被翻牌后进步明显的普小(以及部分略有退步的原重点小学)，具备在未来成为优秀学校的潜质，但目前在成绩或生源方面还有一定的完善空间。 徐汇区 【第一梯队】世界外国语小学、盛大花园小学、爱菊小学、逸夫小学、建襄小学、高安路一小、向阳小学、汇师小学 【第二梯队】上海小学、上师大一附小、东安路第二小学、园南小学、田林第三小学、徐汇一中心、田林四小、求知小学、上海师范大学第三附属实验学校、康健外国语小学、东安路二小 【第三梯队】徐汇实验小学、康宁科技实小、交大附小、上实附小、华理附小、徐教院附小、启新小学 黄浦区 【第一梯队】上海实验小学、蓬莱二小、卢湾二中心、黄埔上外 【第二梯队】上师大附属卢湾实验小学、曹光彪小学、徽宁路三小、黄浦一中心、复兴东路三小、卢湾一中心、私立永昌学校、师专附小 【第三梯队】北京东路小学、黄教院附属中山学校、巨鹿路一小、裘锦秋实验学校 静安区 【第一梯队】一师附小、静教院、静安一中心
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2009年中国水资源公报 2012-04-26 中华人民共和国水利部 2009年，我国气候异常，一些地区降雨之多、台风之强、旱情之重为历史 罕见。旱情来得早、去得晚、范围广、影响大，特别是冬麦主产区年初的冬春连旱，东北西部、华北北部和西北东部的夏伏旱，江南大部、华南大部和西南局部的秋冬连旱，对农业生产带来严重影响。全年有9个台风在我国沿海登陆，发生强风、暴雨、高潮同时出现的最不利形势。受多次大范围、高强度降雨过程影响，全国有210多条河流相继发生超警戒水位以上洪水。在党中央、国务院的正确领导下，水利部门坚持以人为本，超前部署，科学决策，精心调度，各级地方党委、政府全力以赴，广大军民奋力抗灾救灾，最大程度地减轻了洪涝干旱台风灾害损失。 2009年，党中央、国务院高度重视水利工作，国家把加快水利基础设施建 设作为应对金融危机、扩大国内需求的重要领域。各级水利部门深入学习实践科学发展观，坚决贯彻落实中央保增长、保民生、保稳定的各项决策部署，保持了水利又好又快发展的强劲势头。扩大内需水利基础设施建设取得显著成效，有力地促进了经济平稳较快增长；强力推进十七届三中全会明确的病险水库除险加固、农村饮水安全工程、灌区续建配套与节水改造三大任务，涉及民生的水利问题加快解决；为应对我国水资源短缺、用水效率不高、水污染严重的突出问题，明确提出实行最严格的水资源管理制度，节水型社会建设全面推进；一大批重点水利工程开工建设，创近年来新开工大型水利工程数量历史新高；水利法制建设稳步
推进，依法治水、科学管水能力不断提升。水利工作取得的显著成效，为促进经济平稳较快增长提供了有力支撑。 一、水资源量 降水量 2009年，全国平均年降水量591.1mm，折合降水总量为55965.5亿m3，比常年值偏少8.0%。从水资源分区看，松花江、辽河、海河、黄河、淮河、西北诸河6个水资源一级区（以下简称北方6区）面平均降水量为315.7mm，比常年值偏少3.8%；长江（含太湖）、东南诸河、珠江、西南诸河4个水资源一级区（以下简称南方4区）面平均降水量为1079.7mm，比常年值偏少10.0%。在31个省级行政区中，降水量比常年值偏多的有9个省（自治区、直辖市），其中海南和青海偏多程度约30%；降水量比常年值偏少的有22个省（自治区），其中北京和云南偏少约25%。 地表水资源量 2009年全国地表水资源量23125.2亿m3，折合年径流深244.2mm，比常年值偏少13.4%。从水资源分区看，北方6区地表水资源量比常年值偏少13.1%；南方4区比常年值偏少13.5%。在31个省级行政区中，地表水资源量比常年值偏多的有6个省（自治区、直辖市），比常年值偏少的有25个省（自治区、直辖市），其中黑龙江、上海、青海、海南偏多程度在23%～56%之间，江西、吉林、云南、河南、福建、内蒙古、宁夏偏少程度在25%～37%之间，山西、辽宁、河北、北京偏少程度在45%～62%之间。 2009年，从国境外流入我国境内的水量为154.9亿m3，从我国流出国境的水量为5193.3亿m3，从我国流入国际边界河流的水量为1090.7亿m3,全国入海水量为13960.9亿m3。
2016年北京市高考化学试卷 一、选择题. 1．（3分）我国科技创新成果斐然，下列成果中获得诺贝尔奖的是（）A．徐光宪建立稀土串级萃取理论 B．屠呦呦发现抗疟新药青蒿素 C．闵恩泽研发重油裂解催化剂 D．侯德榜联合制碱法 2．（3分）下列中草药煎制步骤中，属于过滤操作的是（）A．冷水浸泡B．加热煎制C．箅渣取液D．灌装保存 A．A B．B C．C D．D 3．（3分）下列食品添加剂中，其使用目的与反应速率有关的是（）A．抗氧化剂B．调味剂C．着色剂D．增稠剂 4．（3分）在一定条件下，甲苯可生成二甲苯混合物和苯．有关物质的沸点、熔点如表： 对二甲苯邻二甲苯间二甲苯苯沸点/℃138******** 熔点/℃13﹣25﹣476 下列说法不正确的是（） A．该反应属于取代反应 B．甲苯的沸点高于144℃ C．用蒸馏的方法可将苯从反应所得产物中首先分离出来 D．从二甲苯混合物中，用冷却结晶的方法可将对二甲苯分离出来 5．（3分）K2Cr2O7溶液中存在平衡：Cr2O72﹣（橙色）+H2O?2CrO42﹣（黄色）+2H+．用
K2Cr2O7溶液进行下列实验： 结合实验，下列说法不正确的是（） A．①中溶液橙色加深，③中溶液变黄 B．②中Cr2O72﹣被C2H5OH还原 C．对比②和④可知K2Cr2O7酸性溶液氧化性强 D．若向④中加入70%H2SO4溶液至过量，溶液变为橙色 6．（3分）在两份相同的Ba（OH）2溶液中，分别滴入物质的量浓度相等的H2SO4、NaHSO4溶液，其导电能力随滴入溶液体积变化的曲线如图所示．下列分析不正确的是（） A．①代表滴加H2SO4溶液的变化曲线 B．b点，溶液中大量存在的离子是Na+、OH﹣ C．c点，两溶液中含有相同量的OH﹣ D．a、d两点对应的溶液均显中性 7．（3分）用石墨电极完成下列电解实验． 实验一实验二 装 置 现象a、d处试纸变蓝；b处变红，局部褪 色；c处无明显变化 两个石墨电极附近有气泡产生；n 处有气泡产生；…
2018年北京市高考化学试卷 一、选择题（共7小题，每小题6分，共42分．每题只有一个正确选项）1．（6分）（2018?北京）下列我国科技成果所涉及物质的应用中，发生的不是化学变化的是（） A．甲醇低温所 制氢气用于新 能源汽车 B．氘、氚用作“人造太 阳”核聚变燃料 C．偏二甲肼用作发射 “天宫二号”的火箭燃 料 D．开采可 燃冰，将其 作为能源 使用A．A B．B C．C D．D 【考点】18：物理变化与化学变化的区别与联系． 【分析】一般来说，物质的熔点、状态发生改变，为物理变化，而生成新物质的变化属于化学变化，化学变化为原子的重新组合，物质的组成、结构和性质发生变化，但原子不会改变，以此解答该题。 【解答】解：A．甲醇生成氢气，为化学变化，故A不选； B．氘、氚用作“人造太阳”核聚变燃料，原子核发生变化，不属于化学变化的范畴，故B选； C．偏二甲肼用作发射“天宫二号”的火箭燃料，燃烧生成氮气和水，发生化学变化，故C不选； D．可燃冰的主要成分为甲烷，燃烧生成二氧化碳和水，为化学变化，故D不选。故选：B。 【点评】本题为2018年全国卷，题目考查物质的变化，侧重于化学与生活、生产的考查，有利于培养学生良好的科学素养，主要把握化学变化与物理变化的区
别，难度不大。 2．（6分）（2018?北京）我国科研人员提出了由CO 2和CH 4 转化为高附加值产品 CH 3 COOH的催化反应历程。该历程示意图如下。 下列说法不正确的是（） A．生成CH 3 COOH总反应的原子利用率为100% B．CH 4→CH 3 COOH过程中，有C﹣H键发生断裂 C．①→②放出能量并形成了C﹣C键 D．该催化剂可有效提高反应物的平衡转化率 【考点】15：化学反应的实质；H1：有机化合物中碳的成键特征． 【分析】A．原子利用率是指被利用的原子数和总原子数之比； B．甲烷反应后生成乙酸，结合分子中化学键变化法判断； C．图中可知。①→②过程中能量降低，说明为放热过程通过过渡态形成了C﹣C 化学键； D．催化剂改变反应速率不改变化学平衡和反应焓变； 【解答】解：A．图中分析，1mol甲烷和1mol二氧化碳反应生成1mol乙酸，生 成CH 3 COOH总反应的原子利用率为100%，故A正确； B．图中变化可知甲烷在催化剂作用下经过选择性活化，其中甲烷分子中碳原子会与催化剂形成一新的共价键，必有C﹣H键发生断裂，故B正确； C．①→②的焓值降低，过程为放热过程，有C﹣C键形成，故C正确； D．催化剂只加快反应速率，不改变化学平衡转化率，故D错误；
电大《经济数学基础12》历年真题及答案 电大《经济数学基础12》历年真题及答案 一.填空题(每题3分，共15分) 6.函数的定义域是 . 7.函数的间断点是. 8.若，则. 9.设，当 0 时，是对称矩阵。 10.若线性方程组有非零解，则－1 。 6.函数的图形关于原点对称. 7.已知，当0 时，为无穷小量。 8.若，则. 9.设矩阵可逆，B是A的逆矩阵，则当= 。 10.若n元线性方程组满足，则该线性方程组有非零解。 6.函数的定义域是 . 7.函数的间断点是。 8.若，则=. 9.设，则1 。 10.设齐次线性方程组满，且，则方程组一般解中自由未知量的个数为3 。 6.设，则= x2+4 . 7.若函数在处连续，则k=2。
8.若，则1/2F(2x-3)+c. 9.若A为n阶可逆矩阵，则 n 。 10.齐次线性方程组的系数矩阵经初等行变换化为，则此方程组的一般解中自由未知量的个数为2 。 1.下列各函数对中，( D )中的两个函数相等. 2.函数在处连续，则（ C.1）。 3.下列定积分中积分值为0的是( A ). 4.设，则( B.2 ) 。 5.若线性方程组的增广矩阵为，则当=（ A.1/2 ）时该线性方程组无解。 6.的定义域是 . 7.设某商品的需求函数为，则需求弹性=。 8.若，则. 9.当时，矩阵可逆。 10.已知齐次线性方程组中为矩阵，则。 1.函数的定义域是 . 2.曲线在点（1,1）处的切线斜率是. 3.函数的驻点是 1.
4.若存在且连续，则 . 5.微分方程的阶数为4 。 1.函数的定义域是 . 2.0. 3.已知需求函数，其中为价格，则需求弹性. 4.若存在且连续，则 . 5.计算积分2 。 二.单项选择题(每题3分，本题共15分) 1.下列函数中为奇函数的是 ( C.）. A. B. C. D. 2.设需求量对价格的函数为，则需求弹性为（ D. ）。 A . B.C D. 3.下列无穷积分收敛的是 ( B. ). A.
哈佛北大精英创立 2018学年上海市宝山区宝山实验学校六年级 第一学期期中考试数学试卷 一、填空题 1. 既是素数又是偶数的是 【答案】2 2. 分解素因数：45= 【答案】533?? 3. 8和9 的最小公倍数是 【答案】72 4. 在18、27、30、44、102中，能被5整除的数是 【答案】30 5. 已知自然数A 与自然数B 是连续的偶数，那么A 、B 的最大公因数是 【答案】2 6. 既是12的倍数又是36的因数的数是 【答案】12.36 7. 如图（1），点A 表示的数是 【答案】4 11 8. = 10 3-54计算 【答案】2 1 9. 是千克的4132 【答案】 6 1 10. 学校教学楼走廊长56米，如果在走廊上等间隔地拜访8盆花，并且走廊的两端各放一盆花，那么每两盆花之间的距离是 米 【答案】8 11. 如图（2），将正方形看做一个整体，那么阴影部分可以用最简分数 来表示
哈佛北大精英创立 【答案】10 12. 三张卡片上分别写有1、2、3三个数字，从这三张卡片中依次抽出两张，就能组成一个两位数，在所得的两位数中，素数有 个 【答案】3 13. 是 按从小到大的顺序排列、、16 5 73.08 3· 【答案】·73.08 3 165ππ 14. 的所有最简分数之和是之间，分母是和在155 4 31 【答案】15 111 15. 的值为 那么如果， ，个数，如分子、分母中较大的那表示，规定对于分数m m m A A A ,12}7 {}3{16}13 16 {3}32{}{=+== 【答案】5 二、填空题 1. 4是8和16的（） 【A 】公因数 【B 】最大公因数 【C 】最小公倍数 【D 】公倍数 【答案】A 2. 的分数有（）个且小于大于6 561 【A 】4 【B 】5 【C 】6 【D 】无数个 【答案】D 3. 如果m 是技术，那么下列数中（）也是奇数 【A 】m+1 【B 】m+2 【C 】m+3 【D 】m+m
2007年中国水资源公报 2008-10-13 2007年，在党中央、国务院的正确领导下，各级水利部门认真贯彻落实科学发展观，积极践行可持续发展治水思路，着力解决水利发展中的突出问题，水利事业保持了投资加大、建设加快，基础增强、管理加强，效益提高、民生改善的良好态势。 2007年，我国极端天气事件频发，水旱灾害呈现先旱后涝、旱涝急转和旱涝并发的局面。淮河发生新中国成立以来仅次于1954年的流域性大洪水，台风前少后多强度大，山洪灾害频发，城市暴雨内涝严重。北方大部及南方一些地区发生冬春连旱，江南、华南等地发生严重夏伏旱，旱情主要发生在粮食主产区和作物生长关键期，波及范围广，持续时间长，影响程度深。面对严重的水旱灾情，党中央高度重视，国务院有关部门周密部署，受灾地区干部齐心合力，军民团结一致，夺取了防汛抗旱工作的全面胜利。 一、水资源量 降水量 2007年全国平均降水量610.0mm，折合降水总量为57763亿m3，比常年值（多年平均值，下同）偏少5.1%。从水资源分区看，松花江、辽河、海河、黄河、淮河、西北诸河六个水资源一级区（简称北方六区，下同）面平均降水量317.9mm，比常年值偏少3.1%；长江（含太湖）、东南诸河、珠江、西南诸河四个水资源一级区（简称南方四区，下同）面平均降水量1128.4mm，比常年值偏少6.0%。在31个省级行政区中，降水量比常年值偏多的有14个省（自治区、直辖市），其中山东和甘肃分别偏多13.8%和11.5%；降水量比常年值偏少的有17个省（自治区、直辖市），其中内蒙古、江西、黑龙江的偏少程度超过20%，北京、广西、河北、湖南、广东、天津偏少15%～10%。
电大【经济数学基础】形成性考核册参考答案 《经济数学基础》形成性考核册（一) 一、填空题 １、、答案：1 2、设，在处连续,则、答案1 ３、曲线＋1在得切线方程就是、答案:y=1/2X＋３/２ 4、设函数,则、答案 5、设,则、答案： 二、单项选择题 １、当时，下列变量为无穷小量得就是（D ） Ａ. Ｂ． C. D. ２、下列极限计算正确得就是( B ） Ａ、B、C、D、 3、设，则( B ). A．B。C。D。 4、若函数f （x）在点x0处可导，则(B）就是错误得. A.函数f （ｘ）在点ｘ0处有定义Ｂ.，但 C.函数f （ｘ）在点x0处连续Ｄ.函数ｆ（ｘ）在点x0处可微 ５、若,则（B)、 A. B. C．Ｄ. 三、解答题 1．计算极限 本类题考核得知识点就是求简单极限得常用方法。它包括： ⑴利用极限得四则运算法则; ⑵利用两个重要极限; ⑶利用无穷小量得性质（有界变量乘以无穷小量还就是无穷小量) ⑷利用连续函数得定义。 (1) 分析:这道题考核得知识点就是极限得四则运算法则。 具体方法就是:对分子分母进行因式分解,然后消去零因子，再利用四则运算法则限进行计算解:原式=== （2） 分析:这道题考核得知识点主要就是利用函数得连续性求极限. 具体方法就是:对分子分母进行因式分解，然后消去零因子，再利用函数得连续性进行计算解:原式== (3） 分析:这道题考核得知识点就是极限得四则运算法则. 具体方法就是:对分子进行有理化，然后消去零因子，再利用四则运算法则进行计算 解:原式==＝= （4) 分析：这道题考核得知识点主要就是函数得连线性. 解:原式= (5)
分析：这道题考核得知识点主要就是重要极限得掌握. 具体方法就是:对分子分母同时除以x ，并乘相应系数使其前后相等,然后四则运算法则与重要极限进行计算 解:原式＝ （6) 分析：这道题考核得知识点就是极限得四则运算法则与重要极限得掌握。 具体方法就是:对分子进行因式分解，然后消去零因子，再利用四则运算法则与重要极限进行计算 解：原式= 2.设函数， 问:（1）当为何值时，在处极限存在? (2）当为何值时,在处连续、 分析：本题考核得知识点有两点,一就是函数极限、左右极限得概念。即函数在某点极限存在得充分必要条件就是该点左右极限均存在且相等。二就是函数在某点连续得概念。 解：(１)因为在处有极限存在，则有 又 即 所以当a 为实数、时,在处极限存在、 (2）因为在处连续，则有 又 ，结合(1)可知 所以当时，在处连续、 3。计算下列函数得导数或微分： 本题考核得知识点主要就是求导数或(全)微分得方法,具体有以下三种: ⑴利用导数(或微分)得基本公式 ⑵利用导数(或微分）得四则运算法则 ⑶利用复合函数微分法 （1),求 分析:直接利用导数得基本公式计算即可。 解： （2)，求 分析:利用导数得基本公式与复合函数得求导法则计算即可。 解:= ＝ （3）,求 分析：利用导数得基本公式与复合函数得求导法则计算即可。 解:23 121 2 1 )53(2 3 )53()53(21])53[(------='---='-='x x x x y （4）,求 分析:利用导数得基本公式计算即可。 解: 分析：利用导数得基本公式与复合函数得求导法则计算即可。 (5）,求
有个快乐地地方教学校 ——赴上海宝山区实验小学学习有感 月日，我有幸同位同仁一起踏上了赴上海学习地列车，到月日回校，共学习一个月.我学习地学校是宝山区实验小学，校长是余慧斌校长.学习期间，我参加了《上海教育和中国教育学会举办地愉快教育研讨会》等三次市、区级大型研讨会，参观了上海一师附小、徐汇区向阳小学、宝山区罗南镇罗南中心小学等所学校，参加学校行政会议次，教师评课活动两次，听课节.在一个多月地学习中，我深深地感受到了学者风范地校长魅力，团结进取地教师群体，现代人格教育地实小品牌，走在前沿地上海教育、海纳百川地上海精神.上海一行，收获颇大，使我受益终身.下面我将我地学习心得向各位领导和老师们做一下汇报：资料个人收集整理，勿做商业用途 第一部分：我眼中地宝山实验小学 一、上海市宝山区实验小学简介 上海市宝山实验小学是一所创办于年地百年老校，学校现有学生人，教师人，个教学班，虽然地处郊区，但却是一所具有科学地教育理念、优秀地教师群体，先进地教学设施，优美地教学环境，一流地教学质量地素质教育学校，是宝山区及上海市小学教育地一颗明珠.资料个人收集整理，勿做商业用途 二、宝山实验小学把“科学地现代人格教育理念”贯穿于学校各项工作之中 宝山实验小学始终坚持“关注儿童主体人格发展”这一理念，为每个学生地人格健康发展服务，从这一理念出发，余校长提出了“高质量、有特色、现代化”地办学目标和“实时现代人格教育”地办学思想，这是余校长对整个学校发展地规划，也是实现“关注儿童主体人格发展”这一理念地方针和策略，宝山实验小学把这一教育理念完美地渗透到了学校地各项工作之中.资料个人收集整理，勿做商业用途 .渗透于学校规划之中：在学校地各种发展规划中，我都找到了“现代人格教育”指导思想地关键词，如学校三年行为规范建设规划中明确指出:“将强化学生个体良好品德行为习惯地养成，探索学生良好心理素质形成地规律与方法和我校人格教育特色和绿色教育项目相结合，形成我校地现代人格教育特色.”文件中是这样规划地，实际也是这样做地.资料个人收集整理，勿做商业用途 .渗透于教学管理之中 刚到实验小学，我很迷惑：“余校长工作既轻松又洒脱，是用什么秘诀抓好学校管理地呢？”原来，学校实施了现代人格教育，不但关注学生人格发展，而且重视教师地人格发展和专业发展，把两者放在比“待遇留人、情感留人”更重要地位置上，学校尊重教师需要，把管理从管束变为引导，从而实现了教学管理地优化活控.即“教师自控、教研组互控、教导处调控、校长室监控、社会家庭协控”，学校重视师师互控地集体协作备课，努力以备课上地创新，实现课堂上地创新.校长室与教导处计划制定地非常细致，从表中可以看出一学期每一周地工作安排.教师们自觉按照计划有序地执行着教学任务，而教导处则严格地指挥着工作地开展.学校每学期组织定期和不定期检查，听取来自学生和社会地反馈意见，然后与教师沟通，积极改进.校长始终站在教学第一线，每学期听课节左右，通过听课检查教学反思，了解学校教学现状，提出意见和改进方向.资料个人收集整理，勿做商业用途 .渗透于各项活动当中 学习期间，我有幸参加了学校地一年级亲子活动，主持活动地是两位一年级地小朋友，那标准地童声普通话、熟练优美地动作、镇定自如地表情，给我留下了深刻地印象，如果不是亲眼所见，很难相信是名一年级地同学.活动地内容有三人绑腿跑，足球射门，三人跳绳，三人接力跑.从活动内容上体现了家长与孩子全家参与、零距离接触地活动教育目地.难怪家长们高兴地说：“我们地参与不仅给孩子带来了欢乐，更重要地是让孩子体会到追求学习、活
水利部二○○二年中国水资源公报 中华人民共和国水利部 2002年，新时期治水思路进一步得到丰富和完善，水利事业发展取得新进展。修订后的《中华人民共和国水法》颁布施行，标志着我国依法治水、依法管水进入新的历史阶段。举世瞩目的南水北调工程历史性地由规划阶段转入实施阶段，长江干堤加固工程基本完工，三峡工程导流明渠截流成功，标志着防洪减灾和水资源配置工程建设取得重大进展。农村饮水解困、大型灌区节水改造、病险水库除险加固和水土保持取得新成绩，水利工程管理体制改革、水价改革等工作取得了实质性进展。水的管理体制改革逐步深化并取得成效，水资源统一调度、节水型社会建设试点、水功能区划、生态环境补水以及建设项目水资源论证等工作，将进一步推进水资源的统一管理、合理配置、高效利用和有效保护。 2002年，我国南方和西北内陆河地区降水量比常年偏多，北方地区降水量比常年偏少。海河、辽河、黄河来水遭遇特枯。南四湖几近干涸，京杭运河济宁段断航50天，辽河干流断流158天。现将2002年的水资源量、蓄水动态、供用水量及江河湖库水质等情况公告如下： 一、水资源量 2002年全国平均年降水量660毫米，折合降水总量62610亿立方米，比常年（多年平均）多3．2％。北方五个流域片（松辽河、海河、黄河、淮河、内陆河）降水量比常年少4．8％（其中海河片比常年偏少26．0％），南方四个流域片（长江、珠江、东南诸河、西南诸河）降水量比常年多7．2％。在各省级行政区中，降水量比常年偏少的有16个省（自治区、直辖市），其中偏少20％以上的有山东、天津、北京、河北、辽宁；比常年偏多的有15个省（自治区、直辖市），其中偏多20％以上的有新疆、湖南、上海、江西。 2002年全国地表水资源量27243亿立方米，折合年径流深287毫米，比常年多4．2％。北方五个流域片地表水资源量比常年偏少27．5％（其中海河片比常年偏少72．4％），南方四个流域片则偏多10．8％。在各省级行政区中，地表水资源量比常年偏少的有15个省（自治区、直辖市），其中偏少50％以上的有天津、山东、河北、北京、辽宁、山西；比常年偏多的有16个省（自治区、直辖市），其中偏多50％以上的是上海和湖南。2002年从国外流入我国境内的水量为278亿立方米，从国内流出国境及流入国际界河的水量共6705亿立方米，入海水量为17693亿立方米。 2002年全国地下水资源量8697亿立方米，大部分与地表水资源量重复，不重复的只有1012亿立方米。将地表水资源量与地下水资源量中的不重复量相加，全国水资源总量为28255亿立方米，比常年多2．9％，其中北方五个流域片水资源总量4158亿立方米，比常年少22．4％，南方四个流域片24097亿立方米，比常年多9．0％。全国产水总量占降水总量的45％，平均每平方公里产水量29．8万立方米。 二、蓄水动态 大中型水库蓄水动态对全国3093座大中型水库统计，2002年水库年末蓄水总量1970亿立方米，比年初蓄水量增加41亿立方米。在九大流域片中，黄河片、海河片和松辽河片分别减少77亿、17亿和16亿立方米，长江片、淮河片和东南诸河片分别增加83亿、46
2020年北京市高考化学试卷 学校:___________姓名：___________班级：___________考号：___________ 1．近年来，我国航空航天事业成果显著。下列成果所涉及的材料为金属材料的是 A．“天宫二号“航天器使用的质量轻强度高的材料——钛合金 B．“北斗三号”导航卫星使用的太阳能电池材料——砷化镓 C．“长征五号”运载火箭使用的高效燃料——液氢 D．“C919”飞机身使用的复合材料——碳纤维和环氧树脂 2．下列物质的应用中，利用了氧化还原反应的是 A．用石灰乳脱除烟气中的SO2 B．用明矾[KAl(SO4)2?12H2O］处理污水 C．用盐酸去除铁锈(主要成分Fe2O3?xH2O) D．用84消毒液(有效成分NaClO)杀灭细菌 3．水与下列物质反应时，水表现出氧化性的是 A．Na B．Cl2C．NO2D．Na2O 4．已知：33As(砷)与P为同族元素。下列说法不正确的是 A．As原子核外最外层有5个电子 B．AsH3的电子式是 C．热稳定性：AsH3 2018年北京市高考化学试卷考点分析答 案详细解析 -CAL-FENGHAI.-(YICAI)-Company One1 2018年北京市高考化学试卷 一、选择题（共7小题，每小题6分，共42分．每题只有一个正确选项）1．（6分）（2018?北京）下列我国科技成果所涉及物质的应用中，发生的不是化学变化的是（） A．甲醇低温所制氢气用于新能源汽车B．氘、氚用作“人造太 阳”核聚变燃料 C．偏二甲肼用作发射 “天宫二号”的火箭燃料 D．开采 可燃冰， 将其作为 能源使用 A．A B．B C．C D．D 【考点】18：物理变化与化学变化的区别与联系． 【分析】一般来说，物质的熔点、状态发生改变，为物理变化，而生成新物质的变化属于化学变化，化学变化为原子的重新组合，物质的组成、结构和性质发生变化，但原子不会改变，以此解答该题。 【解答】解：A．甲醇生成氢气，为化学变化，故A不选； B．氘、氚用作“人造太阳”核聚变燃料，原子核发生变化，不属于化学变化的范畴，故B选； C．偏二甲肼用作发射“天宫二号”的火箭燃料，燃烧生成氮气和水，发生化学变化，故C不选； D．可燃冰的主要成分为甲烷，燃烧生成二氧化碳和水，为化学变化，故D不选。 故选：B。 【点评】本题为2018年全国卷，题目考查物质的变化，侧重于化学与生活、生产的考查，有利于培养学生良好的科学素养，主要把握化学变化与物理变化的区别，难度不大。 2．（6分）（2018?北京）我国科研人员提出了由CO2和CH4转化为高附加值产品 CH3COOH的催化反应历程。该历程示意图如下。 下列说法不正确的是（） A．生成CH3COOH总反应的原子利用率为100% B．CH4→CH3COOH过程中，有C﹣H键发生断裂 C．①→②放出能量并形成了C﹣C键 D．该催化剂可有效提高反应物的平衡转化率 【考点】15：化学反应的实质；H1：有机化合物中碳的成键特征． 【分析】A．原子利用率是指被利用的原子数和总原子数之比； B．甲烷反应后生成乙酸，结合分子中化学键变化法判断； C．图中可知。①→②过程中能量降低，说明为放热过程通过过渡态形成了C﹣C化学键； D．催化剂改变反应速率不改变化学平衡和反应焓变； 【解答】解：A．图中分析，1mol甲烷和1mol二氧化碳反应生成1mol乙酸，生成CH3COOH总反应的原子利用率为100%，故A正确； B．图中变化可知甲烷在催化剂作用下经过选择性活化，其中甲烷分子中碳原子会与催化剂形成一新的共价键，必有C﹣H键发生断裂，故B正确； 经济数学基础形成性考核册及参考答案 作业（一） （一）填空题 1.___________________sin lim 0 =-→x x x x .答案：0 2.设，在0=x 处连续，则________=k .答案：1 3.曲线x y = 在)1,1(的切线方程是.答案： 4.设函数52)1(2++=+x x x f ，则____________)(='x f .答案：x 2 5.设x x x f sin )(=，则.答案：2 π- （二）单项选择题 1. 函数的连续区间是（ ）答案：D A ．),1()1,(+∞?-∞ B ．),2()2,(+∞-?--∞ C ．),1()1,2()2,(+∞?-?--∞ D ．),2()2,(+∞-?--∞或),1()1,(+∞?-∞ 2. 下列极限计算正确的是（ ）答案：B A. B. C. D. 3. 设y x =lg2，则d y =（ ）．答案：B A ．B ．C ．D ． 1 d x x 4. 若函数f (x )在点x 0处可导，则( )是错误的．答案：B A ．函数 f (x )在点x 0处有定义 B ．A x f x x =→)(lim 0 ，但)(0x f A ≠ C ．函数f (x )在点x 0处连续 D ．函数f (x )在点x 0处可微 5.当0→x 时，下列变量是无穷小量的是（ ）. 答案：C A ．x 2 B ．x x sin C ．)1ln(x + D ．x cos (三)解答题 1．计算极限 （1） （2） （3） （4） （5） （6） 2．设函数 ??? ? ???>=<+=0sin 0,0,1sin )(x x x x a x b x x x f ， 问：（1）当b a ,为何值时，)(x f 在0=x 处有极限存在？ （2）当b a ,为何值时，)(x f 在0=x 处连续. 答案：（1）当1=b ，a 任意时，)(x f 在0=x 处有极限存在； （2）当1==b a 时，)(x f 在0=x 处连续。 3．计算下列函数的导数或微分： （1）2222log 2-++=x x y x ，求y ' 答案：2 ln 1 2ln 22x x y x ++=' （2），求y ' 答案： （3），求y ' 答案： （4）x x x y e -=，求y ' 答案： 2010年中国水资源公报 2012-04-26 中华人民共和国水利部 2010年，我国西南五省区发生历史罕见的特大干旱，长江上游、鄱阳湖水系、松花江等流域发生特大洪水，甘肃舟曲发生特大滑坡泥石流灾害，海南、四川两省遭遇历史罕见的强降雨过程，全国有30个省（自治区、直辖市）遭遇不同程度的洪涝灾害。在党中央、国务院的高度重视和正确领导下，国家防汛抗旱总指挥部和水利部超前部署、科学防控，有关部门密切配合、通力协作，广大军民顽强拼搏、团结奋战，成功抗御了西南地区特大干旱，有效应对了严重的洪涝灾害，最大程度地保障了人民群众生命安全，减轻了灾害损失。 党中央、国务院高度重视水利工作，明确提出要下决心加快推进水利建设，进一步明确了新形势下水利的战略地位，以及水利改革发展的指导思想、基本原则、目标任务、工作重点和政策措施。广大水利干部职工迎难而上，顽强拼搏，为水利科学发展注入了新的活力。继续推进农村饮水安全建设，解决了大量农村人口的饮水安全问题，如期完成专项规划内的大中型和重点小型病险水库除险加固任务，加快实施大型灌区续建配套与节水改造，水利发展成果惠及亿万人民群众。着力推进最严格的水资源管理制度，节水型社 会建设试点工作取得成效，水资源调度工作得到进一步强化。《全国水资源综合规划》、《太湖流域水功能区划》获得国务院批复，修订后的《中华人民共和国水土保持法》公布，水利事业快速发展。 一、水资源量 降水量 2010年，全国平均年降水量695.4mm，折合降水总量为65849.6亿m3，比常年值（多年平均值，下同）偏多8.2%。从水资源分区看，松花江、辽河、海河、黄河、淮河、西北诸河6个水资源一级区（简称北方6区，下同）面平均降水量为365.8mm，比常年值偏多11.5%；长江（含太湖）、东南诸河、珠江、西南诸河4个水资源一级区（简称南方4区，下同）面平均降水量为1280.2mm，比常年值偏多6.7%。在31个省级行政区中，降水量比常年值偏多的有20个省（自治区、直辖市），其中新疆、辽宁和吉林等3省（自治区）偏多程度大于30%；降水量比常年值偏少的有11个省（自治区），其中天津、北京和重庆分别偏少18.2%、12.6%和10.6%。 地表水资源量 2010年全国地表水资源量29797.6亿m3，折合年径流深314.7mm，比常年值偏多11.6%。从水资源分区看，北方6区地表水资源量比常年值偏多16.1%；南方4区比常年值偏多10.7%。在31个省级行政区中，地表水资源量比常年值偏多的有19个省（自治区、直辖市），其中辽宁和吉林偏多程度大于80%，海南、浙江、江西、福建、河南、安徽和新疆偏多程度在30%～60%之间；比常年值偏少的有12个省（自治区、直辖市），其中北京、河北、天津、山西和内蒙古偏少程度在30%～60%之间。 2010高考真题精品解析—理综化学（北京卷） 第I卷（选择题共120分） 本卷共20小题，第小题6分，共120分。在每小题列出的四个选项中，选出符合题目要求的一项。 6.下列有关钢铁腐蚀与防护的说法正确的是 A.钢管与电源正极连接，钢管可被保护 B.铁遇冷浓硝酸表面钝化，可保护内部不被腐蚀 C.钢管与铜管露天堆放在一起时，钢管不易被腐蚀 D.钢铁发生析氢腐蚀时，负极反应是Fe－3e－=Fe3+ 6．答案B 7.下列物质与常用危险化学品的类别不对应 ．．．的是 A.H2SO4、NaOH——腐蚀品 B. CH4、C2H4——易燃液体 C.CaC2、Na——遇湿易燃物品 D.KMnO4、K2Cr2O7——氧化剂 7．答案B 【解析】本题考查常见危险化学品的类别。H2SO4和NaOH均具有腐蚀性，属于腐蚀品，A项正确；CH4、C2H4为易燃的气体，属于易燃气体，B项错误；CaC2、Na与水均能剧烈反应，属于遇湿易燃物品，C项正确；KMnO4、K2Cr2O7均具有强氧化性，属于氧化剂，D项正确。 8.下列说法正确的是 A. 的结构中含有酯基 B.顺―2―丁烯和反―２―丁烯的加氢产物不同 C.1 mol 葡萄糖可水解生成2 mol 乳酸（C 3H 6O 3） D.油脂和蛋白质都是能发生水解反应的高分子化合物 8．答案A 【解析】本题考查有机物的结构和性质。为分子间发生 缩聚反应的产物，链节中含有酯基，A 项正确；顺－2－丁烯和反－2－丁烯的加氢产物均为丁烷，B 项错误；葡萄糖为单糖，不能发生水解反应，C 项错误；油脂和蛋白质都能发生水解反应，蛋白质为高分子化合物，但油脂不是高分子化合物，D 项错误。 【误区警示】糖类中的单糖（葡萄糖和果糖）均不能发生水解反应。 9.用右图所示实验装置（夹持仪器已略去）探究铜丝与过量浓硫酸的反应。下列实验不合理．．．的是 A.上下移动①中铜丝可控制SO ２的量 B.②中选用品红溶液验证SO ２的生成 C.③中选用NaOH 溶液吸收多余的SO 2 D.为确认CuSO 4生成,向①中加水，观察颜色 9．答案D 【解析】本题考查铜和浓硫酸的反应。上下移动铜丝可 以控制铜与浓硫酸的接触面积的大小，从而可以控制反应生成SO 2的量，A 项正确；SO 2可使品红溶液褪色，因此②中品红溶液可以验证SO 2的生成，B 项正确；SO 2有毒，能与NaOH 溶液反应，因此③中NaOH 溶液可以吸收多余的SO 2，C 项正确；铜与浓硫酸反应后①中溶液显蓝色即可证明CuSO 4生成，无需向其中加水，D 项错误。 10.下列解释实验事实的方程式不准确．．． 的是 A.0.1 mol/L CH 3COOH 溶液的pH ＞１：CH 3COOH 垐?噲?CH 3COO －+H + B.“NO 2球”浸泡在冷水中，颜色变浅：2NO 2(g) 垐?噲?N 2O 4(g) ?H ＜0 C.铁溶于稀硝酸，溶液变黄：3Fe+8H + +2NO 3- ===3Fe 2+ +2NO ↑+4H 2O D.向Na 2CO 3溶液中滴入酚酞溶液，溶液变红：CO 23-+H 2O 垐?噲?HCO 3-+OH － 10．答案C 【解析】本题考查方程式的正误判断。0.1molCH 3COOH 溶液的pH ＞1，则c(H ＋ )＜0.1mol/L ， 说明醋酸没有完全电离，存在电离平衡：CH 3COOH ?CH 3COO －＋H ＋ ，A 项正确；“NO 2”浸泡在冷水中，温度降低，平衡2NO 2?N 2O 4向正方向移动，颜色变浅，B 项正确；铁容易稀硝酸，溶液变黄，说明Fe 被氧化为Fe 3＋ ：Fe ＋4H ＋ ＋NO 3－ ＝Fe 3＋ ＋NO ↑＋2H 2O ，C 项错误；Na 2CO 3溶液中由于CO32－水解溶液显碱性，加入酚酞，溶液变红，D 项正确。 2018年普通高等学校招生全国统一考试（北京卷） 理科综合能力测试 可能用到的相对原子质量：H 1 C 12 N 14 O 16 6．下列我国科技成果所涉及物质的应用中，发生的不是 ．．化学变化的是 A．甲醇低温 所制氢气用 于新能源汽 车 B．氘、氚用作“人造太阳” 核聚变燃料 C．偏二甲肼用作发射“天 宫二号”的火箭燃料 D．开采可燃冰， 将其作为能源使 用 7．我国科研人员提出了由CO2和CH4转化为高附加值产品CH3COOH的催化反应历程。该历程示意图如下。 下列说法不正确 ．．．的是 A．生成CH3COOH总反应的原子利用率为100% B．CH4→CH3COOH过程中，有C―H键发生断裂 C．①→②放出能量并形成了C―C键 D．该催化剂可有效提高反应物的平衡转化率 8．下列化学用语对事实的表述不正确 ．．．的是 A．硬脂酸与乙醇的酯化反应：C17H35COOH+C2H518OH C17H35COOC2H5+H218O B．常温时，0.1 mol·L-1氨水的pH=11.1：NH3·H2O+ 4 NH+OH? C．由Na和C1形成离子键的过程： D．电解精炼铜的阴极反应：Cu2+ +2e ?Cu 9．下列实验中的颜色变化，与氧化还原反应无关的是 A B C D 实验NaOH溶液滴入 FeSO4溶液中 石蕊溶液滴入氯 水中 Na2S溶液滴入 AgCl浊液中 热铜丝插入稀硝 酸中现象产生白色沉淀， 随后变为红褐色 溶液变红，随后 迅速褪色 沉淀由白色逐渐 变为黑色 产生无色气体， 随后变为红棕色10．一种芳纶纤维的拉伸强度比钢丝还高，广泛用作防护材料。其结构片段如下图 下列关于该高分子的说法正确的是 A．完全水解产物的单个分子中，苯环上的氢原子具有不同的化学环境 B．完全水解产物的单个分子中，含有官能团―COOH或―NH2 C．氢键对该高分子的性能没有影响 D．结构简式为： 电大【经济数学基础】形成性考核册参考答案 《经济数学基础》形成性考核册（一） 一、填空题 1.___________________sin lim =-→x x x x .答案：0 2.设 ? ?=≠+=0,0 ,1)(2x k x x x f ，在0=x 处连续，则________=k .答案1 3.曲线x y =+1在)1,1(的切线方程是 . 答 案: 2 3 21+= x y 4. 设 函 数 5 2)1(2++=+x x x f ，则 ____________)(='x f .答案x 2 5.设 x x x f sin )(=，则__________ )2 π (=''f .答案: 2 π - 二、单项选择题 1. 当+∞→x 时，下列变量为无穷小量的是（ D ） A ． )1ln(x + B ． 1 2+x x C ． 2 1x e - D ． x x sin 2. 下列极限计算正确的是（ B ） A.1lim 0=→x x x B.1lim 0=+→x x x C.11sin lim 0=→x x x D.1sin lim =∞→x x x 3. 设y x =lg2，则d y =（ B ）． A ． 12d x x B ．1d x x ln10 C ．ln10x x d D ．1d x x 4. 若函数f (x )在点x 0处可导，则( B )是错误的． A ．函数f (x )在点x 0处有定义 B ．A x f x x =→)(lim 0， 但)(0x f A ≠ C ．函数f (x )在点x 0处连续 D ．函数f (x )在点x 0处可微 5.若 x x f =)1 (，则=')(x f （ B ）. A ． 2 1x B ．2 1x - C ． x 1 D ．x 1- 三、解答题 1．计算极限 （1）1 2 3lim 221-+-→x x x x 解：原式=)1)(1() 2)(1(lim 1-+--→x x x x x =12lim 1+-→x x x = 2 11121-=+- （2）8 66 5lim 222+-+-→x x x x x 解：原式=)4)(2()3)(2(lim 2----→x x x x x =2 1 423243lim 2=--=--→x x x （3）x x x 1 1lim --→ 解： 原式 = ) 11() 11)(11(lim +-+---→x x x x x = ) 11(11lim +---→x x x x = 1 11lim 0 +-- →x x =2 1- （4）4235 32lim 22+++-∞→x x x x x 解：原式=320030024 23532lim 22=+++-=+++-∞→x x x x x （5）x x x 5sin 3sin lim 0→ 解：原式=53115355sin lim 33sin lim 5 35355sin 33sin lim 000=?=?=?→→→x x x x x x x x x x x （6）) 2sin(4 lim 22--→x x x 解：原式=414) 2sin(2 lim )2(lim )2sin()2)(2(lim 222=?=--?+=--+→→→x x x x x x x x x2018年北京市高考化学试卷考点分析答案详细解析
2016年电大《经济数学基础12》考试题及答案
2010中国水资源公报
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