考研数学选择题

小题狂做

?x(xye?sinxcosx)d??( ) ??D2A 2C 2??xyeD1D1?x2d? B 4??(xyeD1?x2?sinxcosx)d?

??sinxcosxd? D 0

172.设f,则累次积分I?A C

?dx?abxa(x?y)f(y)dy可化为定积分( )

1b1b22(b?y)f(y)dy(y?a)f(y)dy B ??aa22?ba(b?y)2f(y)dy D

?ba(y?a)2f(y)dy

173.设D1是以O(0,0),P(a,0),Q(0,a)为顶点的等腰直角三角形,D2是中心在点(1,0)半径R?1的半圆,且半圆与直角边PQ相切与点M,若积分区域D是从D1中挖去D2的区域,则

??ydy?( )

D52?2 B 63512 D C ?62A 174.

25?2 3615?2 26?10dy?1y1?x2ydx?( )

1(2?1) 31(3?1) 21(2?1) B 31C (3?1) D 2A

22175.设积分区域D?(x,y)|x?y?2x?2y,则

??22(x?xy?y)d??( ) ??DA 6? B 8? C 10? D 12?

22176.设区域D?(x,y)|x?y?2x,则

????Dxd??( )

A

321532152 D 2 B C 15321532177.设x?rcos?,y?rsin?,则在极坐标系(r,?)中的累次积分直角坐标系(x,y)中的累次积分( )

??20d??11cos??sin?f(cos?,sin?)dr可化为

A

??10dx?dx?1?x21?xf(x.y)dy B

?10dx?1?x2f(x.y)x?y221?xdy

C

11?x20xf(x.y)dy D

?10dx?1?x2f(x.y)x?y22xdy

小题狂做

178.设积分区域D??(x,y)|0?x?1,0?y?1?,则二重积分I?d??( ) 2232??(1?x?y)DA

???? B C D 2346179.设D?(x,y)|x?y?1,x?y?9,x?3y,y?3x,则

?2222?yarctand??( ) ??xD???2?2A B C D 6363180.设积分区域D由y?x与x?y2围成,则

sin?yd??( ) ??yD1A

? B ?? C

? D ?1?

222181.设f(x,y)为连续函数,且D?(x,y)|x?y?t,则lim???t?01?t2??f(x,y)d??( )

DA f(0,0) B ?f(0,0) C f'(0,0) D 不存在 182.设有一半径为R的圆盘,其中心在坐标原点处,圆盘上任一点(x,y)处的密度?(x,y)与该点到点

(R,0)的距离的平方成正比,比例常数k?0,则该圆盘的重心坐标是( )

A (0,?) B (0,?R4RRR) C (?,0) D (?,0) 343183.设y?y(x)在[0,??)可导,在任意x?(0,??)处的增量?y?y(x??x)?y(x)满足

?y(1??y?)y?x??,其中?当?x?0时是?x等价的无穷小,又y(0)?1,则y(x)等于( ) 1?x)?1] B ln(1?x)?1 A (1?x)[ln(1?xC

11(?1?x) D 1?x 21?xx184.设[f(x)?e]sinydx?f(x)cosydy是一个二元函数的全微分,且f(x)具有一阶连续导数,

f(0)?0,则f(x)等于( )

ex?e?xex?e?x?1 B 1?A 22e?x?exex?e?xC D

22小题狂做

22185.设y?y(x)是微分方程(y?( ) A

x?y)dx?xdy满足初值y(1)?0的特解,则

?21y(x)dx?3231 B C D 4323x???186.设y?y(x)是y''?by'?cy?0的解,其中b,c为正常数,则limy(x)?( ) A 与解y(x)的初值y(0),y'(0)有关,与b,c无关 B与解y(x)的初值y(0),y'(0)及均b,c无关 C与解y(x)的初值y(0),y'(0)及c无关,只与b有关 D与解y(x)的初值y(0),y'(0)及b无关,只与c无关

''2187.若A、B为非零常数,C1、C2为任意常数,则微分方程y?ky?cosx的通解应具有形式

( )

A C1coskx?C2sinkx?Asinx?Bcosx B C1coskx?C2sinkx?Axcosx C C1coskx?C2sinkx?Axsinx

D C1coskx?C2sinkx?Axsinx?Bxcosx

188.设线性无关的函数y1,y2,y3都是二阶非齐次线性微分方程y?p(x)y?q(x)y?f(x)的解,

'''C1,C2是任意常数,则该非齐次方程的通解是( )

A C1y1?C2y2?y3 B C1y1?C2y2?(C1?C2)y3 C C1y1?C2y2?(1?C1?C2)y3 D C1y1?C2y2?(1?C1?C2)y3

189.设a,b,c为常数,则微分方程y?3y?2y?3x?2e的特解的形式为( ) A (ax?b)e B (ax?b)xe C (ax?b)?ce D (ax?b)?cxe

xxxx'''x小题狂做

190.设C1,C2是两个任意常数,则函数y?C1e2x?C2e?x?2xe?x满足的一个微分方程是( ) A y'?y'?2y?6e?x B y''?y'?2y?6e?x C y''?y'?2y?3xe?x D y''?y'?2y?3xe?x

191.设C1,C2,C3是三个任意常数,则方程y'''?y''?y'?y?0的通解形式为( ) A C1ex?C2cosx?C3sinx B C1e?x?C2cosx?C3sinx C C1e2x?C2cos2x?C3sin2x D C1e?2x?C2cos2x?C3sin2x

192.设f1(x),f2(x)为二阶常系数线性微分方程y?py?qy?0的两个特解,C1,C2是两个任意常数,则C1f1(x)?C2f2(x)是该方程通解的充分条件( ) A f1(x)f1'(x)?f2(x)f2'(x)?0 B f1(x)f2'(x)?f2(x)f1'(x)?0 C f1(x)f2'(x)?f2(x)f1'(x)?0 D f1(x)f2'(x)?f2(x)f1'(x)?0

193.已知曲线y?y(x)经过原点,且在原点的切线平行于直线2x?y?5?0,而y(x)满足微分方程

'''y''?6y'?9y?e3x,则此曲线的方程为( )

A y?sin2x B y?C y?122xxe?sin2x 2x(x?4)e3x D y?(x2cosx?sin2x)e3x 2?1?(y')2?2yy'',194.初值问题?的特解是( ) 'y(1)?1,y(1)??1,?A y?121(x?4x?5) B y?(x2?3x?4) 2222C y??x?x?1 D y?x?3x?3

''''''195.二阶常系数线性微分方程y?8y?25y?0满足初值y(0)?1与y(0)??4的特解y等于

( ) A e?3xcos4x B e3xcos4x

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