国开网高等数学基础线下形考作业二

国开网高等数学基础线下形考作业二（精简篇）《高等数学基础》第二次作业（一）单项选择题

第3章导数与微分f(00且极限

f(x存在，则

f(x)（C ）．x0 x x0 xA. f(0) B. f(0)C. f(x) D.0cvxf(xx0

可导，则h0

f(x0

2h)f(x02h

（D ）．A. 2f(x) B. f(x)0 0C. 2f(x) D. f(x)0 0fx)ff(x)exlimx0 x

（A ）．A. e B. 2eC. 1e D. 1e2 4f(x)x(x1)(x2) (x99)f(0（D ）．A.C.9999!B.D.9999!⒌下列结论中正确的是（C）．f(xxx可导．0 0f(xxx可导．0 0f(xxx有极限．0 0f(xxx连续．0 0（二）填空题 1f(xx2sinx0,

, x0，则f(0) 0 ．x0df(lnx) 2ln x 5⒉设f(ex)e2xx，则 ．dx x xf(x

1在2处的切线斜率是kxπx

122 2 ⒋曲线f(x)sinx在( ,处的切线方程是y x )4yx2xy2x2xlnx)

2 2 4yxlnxy1x（三）计算题⒈求下列函数的导数y：3 3 1x⑴y(xxx

y(x3)ex

x2ex2⑵ycotxx2lnx ycsc2xx2xlnx⑶y

x2lnx

y

2xlnxxln2x⑷y

cosx2xx3

y

x(sinx2xln2)x2x)x41⑸y1

lnxx2

y

sinx( 2x)(lnxx2)cosxsinx sin2x⑹yx

sinxlnx y4x3

sinxx

cosxlnx⑺y

sinxx2

y

3x(cosx2x)(sinxx2)3xln33x 32x⑻ye

tanxlnx yex

tanx

ex cos2x ⒉求下列函数的导数y：x2x2x21xx21x2⑵ylncosx3sinx3y 3xcosx3

3x2tanx3x x x⑶yx x x7yx87

y

7 1x 8x83x3x xy

1(x

1 2x2)3

1 1x2)3 2⑸ycos2exyexsin(2ex)⑹ycosex2⑹y2xex2sinex2⑺ysinnxcosnxynsinn1xcosxcosnxnsinnxsin(nx)⑻y5sinx2y2xln5cosx25sinx2⑼yesin2x⑼ysin2xesin2x⑽yxx2 ex2⑽yxx2(x2xlnx)2xex2⑾yxex eex⑾xy xex(exx

exlnx)eexex⒊在下列方程中， 是由方程确定的函数，求 ：⑴ycosxe2yycosxysinx2e2yyy ysinxcosx2e2y⑵ycosylnxysiny.ylnxcosy.1xy cosysinyln⑶2xsinyx2y2xcosy.y2siny2yxx2yy2

y(2xcosyx2)y2

2y2

2sinyy 2xy2ysiny2xy2cosyx2⑷yxlnyyy1yy yy1⑸lnxeyy21eyy2yyxy 1x(2yey)⑹y21exsiny2yyexcosy.ysiny.exy

exsiny2yexcosy⑺eyexy3eyyex3y2yy

e 3y2xeyx⑻y5x2yy5xln5y2yln2y

5xln512yln⒋求下列函数的微分dy：⑴ycotxcscx1 cosxdy⑵y

)dxcos2x sin2xlnxsinx1sinxlnxcosxdyx dxsin2x⑶yarcsin1(11(1xx)21x)2

11

x)

1x211x21x x)231x31x1xlny

1x)x)3y

1 1 1( )y 31x 1xy

( 1 1 )1 1x3 1x1 1x3 1x3⑸ysin2exdy2sinexex3exdxsinex)exdx⑹ytanex3dysec2ex33x2dx3x2ex

sec2xdx⒌求下列函数的二阶导数：⑴yxlnxy/r/