【经济数学基础】形考作业参考答案.doc

【经济数学基础】形考作业一答案:(一)填空题xsinx___________________limx0x答案:0设2x1,x0f,在x0处连续,:1(x)k,x011曲线yx在(1,1):yx22设函数f(1)22x5,则f(x):2xxxπ设f(x)xsinx,则)__________f(2π2(二)单项选择题函数x,下列变量为无穷小量是(D)(1x)B./(B),则dy(B).(x)在点x0处可导,则(B)(x)()xx0,但Af(x0)(x)(x)在点x0处可微1若(x,则f'(x)(B)f).-1/(三)(1)2xlimx1x23x2112(2)2x5xlim2x2xx668121(3)1xlimx0x112(4)limx2x23x3x2x5413(5)sin3xlimxsin50x352x4(6)4limxsin(2),x0xf,(x)a,x0sinxxx0问:(1)当a,b为何值时,f(x)在x0处有极限存在?(2)当a,b为何值时,f(x):(1)当b1,a任意时,f(x)在x0处有极限存在;(2)当ab1时,f(x)在x0处连续。:(1)yx2x2,求y答案:2logx22xy2x2ln2x1ln2(2)axby,求y答案:cxdyadcb)(cxd2(3)1y,求y答案:3x5y2(3x335)(4)xye,求y答案:xx1y(x1)e2xx(5)ybxaxaxe,求dy答案:dyabxbbxdxsine(sincos)1111(6)yxxex,求dy答案:dyx)dx(xe22x(7)sinx22xx)dycosxe,求dy答案:dyx(2xe2x(8)yxnxnn1sin,求y答案:(sincoscos)sinynxxnx(9)ln(1)2y,求y答案:xxy121x(10)y132sin12xxx2x,求y答案:1sin3x2ln2112yxx1262xcosx56下列各方程中y是x的隐函数,试求y或dyy32x(1)2yxy3x1x,求dy答案:dydx22yx2xy4yecos(xy)(2)xyexxysin(,求y答案:)4yxyxecos(xy):(1)ln(1)2y,求y答案:xy222x22(1x)(2)y1xx5331,求y及y(1)答案:22y,y(1)1xx44【经济数学基础】形考作业二答案:(一)填空题若f(xxxc,则f(x):2ln22xx)d22(sinx):sinxc1若f(x)dxF(x)c,则xf(1x2):F(1x)c22de设函数ln(12):001若tP(x)dx21t,则P(x):11x2(二)单项选择题下列函数中,(D).-2cosx2D.-cosx122cosx下列等式成立的是(C).1lnxdxd((cosx)B.)(2),常用分部积分法计算的是(C).(2x1)dx,(D)..sinxdx0x/23下列无穷积分中收敛的是(B).(三)解答题计算下列不定积分x3x3(1)xdxexe=c3lne2(1x)(2)xdx3542=xx2x2c2352x4(3)xdx212=x2xc21(4)xd12x1=ln12xc231(5)x2x2dx=x2)c2(23sinx(6)xdx=2cosxcxxxx4(7)x2(8)ln(x1)dx=(x1)ln(x1)xcxsind=cossinc222计算下列定积分12(1)1xdx1=52x2e(2)xd21x=ee3e1(3)xd1x1lnx=2(4)xcos2xdx20=12e(5)xlnxdx1142(6)xx)d