2022年微积分习题-答案2.docx

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1、精选学习资料 - - - - - - - - - 习题 1-8 名师归纳总结 1 1lim x 0tan3x3lim 3 x0tan3x3x第 1 页,共 6 页x3x2 lim xxsin11lim / x0sin11xx1/x3 lim x 0xcotxlim x 0xx1tan4 lim x 0tanxxsinxlim x 0tanxlim x 0sinx110xx5 lim x 01xcos2xlim x 01 12sin2x sinxxsinxlim x 02sinx2x6 lim x 01xxlim x 01 1xsin2cos22lim x 02x2xxlim / 20x/21s

2、insinx22- - - - - - -精选学习资料 - - - - - - - - - 7 lim xsinxlim xsinxxlim xsinx1x0x 8 令tarcsinx,就xsint,就lim x 02arcsinx3 x名师归纳总结 2lim t 032 tt202 e1第 2 页,共 6 页sin39 lim x 0xsinxlim x 01sinx/x11xsinx1sinx/x11 1lim 1x 0x 1 /xlim x 0 1x1/x1e1x22 lim 1x 02x 1 /xlim x 0 121 x /2x22 e 3 lim x1 xx2 xlim x 112

3、xlim x 11xx4 lim x 11kxlim x 11xkekxx1 12 5 lim xxx1x3lim x 1x1 1x1 1 1xlim x 1x1 1x1 1lim x 1x1 12e11e6 lim xxaxlim x 12 axxaxalim x 12 axa /2 a2 a 12 aaxaxa2 ae12 ae- - - - - - -精选学习资料 - - - - - - - - - 7 lim 1x 0xex1 /xlim x 0 1xex1/xexex名师归纳总结 lim x 0eexex1/xtlim x 01 11 x1/2x第 3 页,共 6 页 8 lim x

4、 0e1ln1xlim x 01x1x1xxlim 1/ x1/x11/2x,1/x1lim t1t/2sin1令t1,就lim x 0e1ln1xx1xxt1lim t1t21 t1 /2121/2et1故lim x 01ln1x114x1x5x5 9 lim x5x21sin1lim x3 x1x399 3 xx5005333x0,x1011- - - - - - -精选学习资料 - - - - - - - - - 故fxsinx,x11x 2,x名师归纳总结 4lim x1fx1,x1c eln3第 4 页,共 6 页xlim x1s i n1xlim xxcx/2lim x 12 cx

5、/2xcxc2 ccxcc 12cc5lim x 12c2xxcxccx/23,即c e3,故lim xxc1n212.n21n 1nn2- - - - - - -精选学习资料 - - - - - - - - - n11.1n2n2n2名师归纳总结 6故lim nnn21n212.n21n11第 5 页,共 6 页n n21n212.n21n1nn21nn21n.n21n故lim nnn21n212.n21nlim nnn2nnlim n11/n1xx,limn12 当x0 时,n1x1当1x0 时,1xn1x01xx1,limnlimn1xlimn1x0x1x0x0故lim x 0n1x1设x n22.- - - - - - -精选学习资料 - - - - - - - - - 假设x n存在极限,就,limnx n1lim nx n名师归纳总结 7x n12x n,即2x nx n第 6 页,共 6 页就x n2 舍去x n-1 故数列x n存在极限,limnx n2本利和6% 2000 e206640 元812006.5% Pe16得P4245000006% Pe20得P15059.719- - - - - - -