填空题 数学660题

小题狂做

高等数学填空题

?4?x2,x?0,?x2?1,x?0,311.设g(x)??则g(f(x))? f(x)??2?4?x,x?0,??x,x?0,x3ex(3ex?1)312.I?lim? x???[1?(ex?1)2](1?ex)313.设xn?(1?111)(1?).......(1?)，则limxn? 242nx??222n?n?1xn? 314. 设xn????，则limx???k?12(1?2?.....?k)?315.设??0,??0为常数，则I?limxex?????x? 316.I?lim(sinx??21?cos)x? xxx22?31317.I?lim(x)x? xx?02?3x2(1?cosx)(1?3cosx)......(1?ncosx)318.I?lim?

x?0(1?cosx)n?1319.设a?0,a?1，且I?limx(a?ax???p1x1x?1)?lna，则p?

320.I?limx?0x??cost2dt02x2sin10x6656? 65321.I?lim(x?x?x?x)? x???1x322.设a,b,p为非零常数，则I?lima?besinpx?? 1x?0|x|a?bexf(x)1f(x)13x)?e，则lim(1?)x? 323.设lim(1?x?x?0x?0xx324.设a1,a2,...am为正数(m?2)，则I?lim(a?a?......?a)?

x??n1n21nnm325.[x]表示x的最大整数部分，则limx[]? x?02x326.设?an?为数列，liman?1?q,|q|?1，则liman?

n??n??an小题狂做

327.数列xn?n[e(1?)n??1n?n?1]，则limxn? n??nn328.设limxn?a，则当a?1时limxn? ，当|x|?1时limxn?

n??n??112329.I?lim2{ln(1?2x?x)?6[(1?x)3?1]}?

x?0x330.极限I?limn??0?ln(1?x)dx? ?xa1n331.设f(x)连续，x?a时f(x)是(x?a)的n阶无穷小，则x?a时 阶无穷小 332.已知当x?0时F(x)?f(t)dt是(x?a)的

?x?sinx0ln(1?t)dt是xn的同阶无穷小，则n? 1x333.设函数f(x)在x?1连续，且f(1)?1则limln[2?f(x)]?

x????ln(1?x2)?334.设f(x)??1?x2?Aearctanx?(???x?1)(1?x???),f(x)在(??,??)处连续，则A?

1?x?2?e?ln(1?2x)?b,x?0,2?xx1?e??335.f(x)??a,x?0,则a? ，b? 时，f(x)在x?0处连续

?11??,x?0,22sinxx???ex?b336.设f(x)?有无穷间断点x?e，可去间断点x?1，则(a,b)?

(x?a)(x?b)?x3,(x??1),?x2,(x?0),?337.设f(x)??2?x,(?1?x?0),g(x)??则limf(g(x))?

?x,(x?0),x?0??2?x,(x?0),?338.设f(x)在(??,??)定义，f(0)?1且f(x)在x?0处连续，并满足f(2x)?f(x)，则在(??,??)上f(x)?

339.设a0?0,an?an?1(an?1?1)(n?1,2,......)，则liman? n??小题狂做

arctanx,x?1.??340.设f(x)??1x2?1则f'(x)? ?(e?x)?,x?1,??24x341.函数f(x)满足f(0)?0,f'(0)?0，则J?lim?x?0f(x)? ?arctanx,x?0,?342.设f(x)??则f'(x)? x?x?0,?1,343.设f'(1)?1，则I?limx?0f(1?x)?f(1?2sinx)?

x?2sinx1n11?cos1n? 344.设f(x)在x?0可导且f(0)?1,f(0)?3，则数列极限I?lim(f())n??n'1?2d?xarctan,x?0,f[?(x)]? 345.设?(x)??f(x)可导，则xdx2??ln(1?x),x?0,346.当sinx?0,cosx?0时y?(sinx)cosx?logsinxcosx，则y?

347.设可导函数f(x)的原函数是F(x)，可导函数g(x)的原函数G(x)，g(x)与f(x)互为反函数，则

'dF(g(x))dG(f(x))?? dxdx348.曲线y?aex与y?x有公切线，则公切线的切点的横坐标x? f(a?h)?f(a)?f'(a)h349.设f(x)在x?a处二阶导数存在，则I?lim?

h?0hx?sintsint?)sinx，则曲线在x?处的切线方程为 350.设曲线f(x)?lim(t?xsinx2

351.设函数f(x)在x?0处连续，且lim f(x)?2则曲线y?f(x)在x?0处的法线方程为

x?0ex?11?2dyd2y?x?ln(1?t)? ，2? ，y?y(x)352.设y?y(x)由参数方程?确定，则2dxdx?y?arctant?在任意点处的曲率K?

小题狂做

d2y353.设y?y(x)由方程y?sin(x?y)确定，则2?

dxd2ydy?bx?cy?0简化为 354.作变量替换x?e，方程ax2dxdxt2355.设y?xcosx，则y(n)? 356.设f(x)?x100ex，则f(200)(0)?

'357.设有界函数f(x)在(c,??)内可导，且limf(x)?b，则b?

x???2358.设函数f(x)在(a,??)内可导，且任意x?(a,??)有|f'(x)|?M(M为常数)，则

f(x)?

x??x2222)? 359.数列极限I?limn(arctan?arctann??nn?1lim(x?3)2360.函数y?的单调增区间是 ，单调减区间是 ，极值

4(x?1)是 ，凹区间是 ，凸区间是 361.设y?y(x)二阶可导，且

dy?(4?y)y?(??0)，若y?y(x)的一个拐点是(x0,3)，则 dx??

362.设f(x)?xe，则fx(n)(x)在x? 处取极小值

322363.设y?y(x)是由方程2y?2y?2xy?x?1确定的，则y?y(x)的极值点是 2?3364.设f(x)?3x?Ax(x?0),A为正常数，则A 至少为 时，有f(x)?20(x?0)

32365.函数f(x)?|4x?18x?27|在[0,2]上的最小值等于 ，最大值等于 366.函数f(x)?367.I??x01?sintdt在[0,?]上的值域是

dx?x2(1?x4)?

368. I?369. I??3?2xdx? 3?2xdx?sin4x?cos4x? 小题狂做

370. I?sinx?sinx?cosxdx?

371. I?x?1?2?(x?1)2?x?1dx?

372. I??xex1?exdx?

x4?1dx? 373. I??1?x6374.设a?0则I?375. I??a?ax?1?x2a?xlndx? 322?(012x?x2?(1?x2)3)dx? x1t2376.设limdt?c，则a? ，b? c?

2x?0sinx?ax?b1?t377.设f(x)??x20e?tdt，则f(x)的极值为 ，f(x)的拐点坐标为

2x22x?1F(x)?[(?lnx)?(?lnt)]f(t)dt,(x?1)的极小378.设f(x)是定义与的正值连续函数，则?1xt值点是x?

1dtdtx?379.设F(x)???01?t2,(x?0)则F(x)? 01?t2x380.设f(x)?x?x22?20f(x)dx?2?f(x)dx，则f(x)?

01?xe?x,x?0,4?381.f(x)??，则f(x?2)dx? 1?1,?1?x?0,??1?cosx382.I??121?2(xarcsinx1?x2?sinx1?x2)dx?

383.f(x)?384.I?1,x?[0,?]则f(x)在[0,?]上的全体原函数是 21?sinx?1dx1?e1x?1? 385.I???0xcos2x?cos4xdx?

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