題號一二三四五六七八九十十一十二總成績得分一、填空題(每空3分,共15分) _____________________1.f(x)=lg(3-x)的定義域是 _____________________EQ\*jc3\*hps28\o\al(\s\up2147483647(m),喻1)EQ\*jc3\*hps26\o\al(\s\up9(2),2)EQ\*jc3\*hps26\o\al(\s\up9(x),x)EQ\*jc3\*hps26\o\al(\s\up9(3),1)5.設(shè)可微函數(shù)y由方程x3+y5-1.設(shè)f(x)=xcosx,則答:()(A)f(x)在(-m,+m)內(nèi)有界;(D)f(x)在x喻m時為無窮小。(B)當(dāng)x喻0時，tanx-x,sinx-x，故EQ\*jc3\*hps26\o\al(\s\up0(lim),x喻0)=EQ\*jc3\*hps26\o\al(\s\up0(lim),x喻0)=0;(C)當(dāng)x喻0時，tanx-x,sinx-x，故EQ\*jc3\*hps24\o\al(\s\up0(lim),x喻0)EQ\*jc3\*hps24\o\al(\s\up8(s),t)EQ\*jc3\*hps24\o\al(\s\up8(i),a)EQ\*jc3\*hps24\o\al(\s\up8(n),n)EQ\*jc3\*hps24\o\al(\s\up8(2),5)EQ\*jc3\*hps24\o\al(\s\up8(x),x)=EQ\*jc3\*hps24\o\al(\s\up2(lim2),x喻05)EQ\*jc3\*hps24\o\al(\s\up8(x),x)=EQ\*jc3\*hps24\o\al(\s\up8(2),5);x喻03.若f(x)在點(diǎn)x=x0處可導(dǎo)，則有答:()(A)EQ\*jc3\*hps23\o\al(\s\up2147483645(l),h)EQ\*jc3\*hps23\o\al(\s\up2147483645(im),喻0)f(x0+2EQ\*jc3\*hps23\o\al(\s\up4(h),h))-f(x0)=f,(x0);(B)EQ\*jc3\*hps26\o\al(\s\up2147483646(l),h)EQ\*jc3\*hps26\o\al(\s\up2147483646(im),喻0)f(x0-h-f(x0)=f,(x0);(C)EQ\*jc3\*hps24\o\al(\s\up2147483644(l),h)EQ\*jc3\*hps24\o\al(\s\up2147483644(im),喻0)f(x0)-EQ\*jc3\*hps24\o\al(\s\up3(f),h)(x0-h)=f,(x0);(D)EQ\*jc3\*hps23\o\al(\s\up2147483647(l),h)EQ\*jc3\*hps23\o\al(\s\up2147483647(im),喻0)f(x0+h)EQ\*jc3\*hps23\o\al(\s\up6(-),h)f(x0-h)=f,(x0)。(A)增加，曲線y=f(x)為凹的;(B)減少，曲線y=f(x)為凹的;(C)減少，曲線y=f(x)為凸的;(D)增加，曲線y=f(x)為凸的。(A)如果(x0,f(x0))是f(x)的拐點(diǎn),則必定f,,(x0)=0;(B)如果f,,(x0)=0,則(x0,f(x0))必定是f(x)的拐點(diǎn);(C)如果(x0,f(x0))是f(x)的拐點(diǎn),則必定f,,(x0)不存在;(D)如果f,,(x0)=0,則(x0,f(x0))有可能是f(x)的拐點(diǎn)。三、計(jì)算下列極限9分）EQ\*jc3\*hps28\o\al(\s\up17(nt),x)EQ\*jc3\*hps29\o\al(\s\up2(im),喻0) 1 1cosudu,求dy,d2EQ\*jc3\*hps30\o\al(\s\up3(y),2)；0sinududxdx3.(5分)設(shè)y=f(ex)ef(x)，求dy。2f(x)=〈|1ln2)在x=0處連續(xù),試確定常數(shù)a,b。六、計(jì)算下列積分（15分）:1.(5分)求dx；(x+2)4-x2dx；3.(5分)已知f(x)的一個原函數(shù)是arcsinx,求∫xf,(x)dx。七、(4分)設(shè)f(x),g(x)在[a,b]上連續(xù),且f(a)<g(a),f(b)>g(b),證明在(a,b)內(nèi)必存在一點(diǎn)ξ,使得f(ξ)=g(ξ)。八、計(jì)算題11分）1.(6分)設(shè)y(x)是可導(dǎo)函數(shù),