高等数学基础作业2.doc

高等数学基础作业2.doc高等数学基础作业2第3章导数与微分—:单项选择题1:设/(())=()且极限lim山存在,则lim山二(b)xtO入 a->0XA:/(())B:广(O)C:f\x)D:02:设/(x)在心可导,则lim八电-专7九L(D)方to 2hA:-2广(心) B:广(Jr。) C:2广⑴) D:-广(Jr。)3:设曲★,则恤几+节)7叭(a)心tO 心A:eB:2eC:—eD:—e2 44:设/⑴=心一於-2)……(x-99),则广(O)=(D)A:99B:-99C:99!D:-99!5:下列结论中正确的是(C)A:若/(兀)在点兀o有极限,则在点石)可导。B:若/(X)在点X。连续,则在点心可导。C:若/(兀)在点兀°可导,则在点兀)有极限。D:若/(兀)在点兀。有极限,则在点X。连续。填空题2 • 1 r\1:设函数/&)=,则广(0)=00;x=02:设论卜戶+5/,则如L处凹dx X3:曲线/(x)=VI+l在(1,2)处的切线斜率是+III4:曲线/(x)=sinx在-,1处的切线方程是y=l5:设y=x2x,则y=2(lnx+l>2x6:设y=xlnx,则yN=—X三:计算题1:求下列函数的导数VOy=(xVx+解:yr=-x^ex +3丄|+-x2+3e2/(2)y=cotx+jc2lnx解:yf=esc2x+2xlnx+xr2◎72x\nx-x2-gt\解: _M21nA-l)In2a:In2xx3解:cosx+2A)3x2_a:(-sinx+2'In2)-3(cosx+T)解:lnx-x2sinx——2xsinx—l无 丿• 9sirrx(lnx-x2)cosx(6)y=x4-sinxlnx解:严・?3V(仝sinx+x^(7)y=竝,_(cosx+2x)3A-(sinx+x2解:y=-32x)3Tn3_(cosx+2x)-(l_ 3Asinx+x2)ln3(8)y=extanx+Inx解:y'=extanx+eAsec2x+—=(tanx+sec2 +—x x2:求下列函数的导数Vo(1)),=严解:yf=e^02yfx(2)y=Incosx解:7(cosx)= x(-sinx)=-tanxCOS兀y=sin2xf解:yr=2sinA(sinx)=2sinxcosx=sin2xy=sinx2解:yr=cosx2x(%2)=2xcosx2⑹y=cos"解:y'=-sin/x(『)=-eAsin^AsirTxcosmx解:yr=Hsin/?_,xcosxcosnx-ns\nnxsmnx解:=5sinvIn5x(sinx)=5s,nvxIn5xcosx(9).V=COSA解:)r=护。sxx(cos%)':在下列方程中,y=y(x)是由方程确定的函数,求八(l)ycosx=e2'解:yrcosx+yx(-sinx)=e2yx2yf=>yf=ysinxcosx-2(?2v(2)y=cosyInx解:沁~皿+沁》=Tx (1+sinyinx)x工2(3)2xsiny=—.2xy-2y2siny=>y=—二一: v2xycosy+y解:2siny+2xcosyxyr-瓯'兀•'(4)y=x+Iny解:yr=1+—^>yy