江西财经大学10-11学年第二学期期末考试微积分2试卷

江西财经大学

10－11学年第二学期期末考试试卷

试卷代码：12004A 授课课时：64

课程名称 calculus 适用对象：10级国际学院本科生

试卷命题人 聂高辉 试卷审核人

1. Full in the blank of each statement in the following five statements such that the statement is right. Then write the corresponding answer on the answer book by the title number. You can be gained 3 points for the right thing on per blank.

(1) （x,y)?(0,2)limy= x+y222(2) d(x+y+z)|(1,1,1)=

(3)

-x-yedA= , whereD（x,y)|0?x,0?y. ??D??(4) The general solution of the equation yn?2?5yn?1?6yn?2?0is

1(5) The region of convergence of series ?x?1is (n?1)n?0?2. Choose the one that the statement is right from four choices marked A, B, C,

and D, with which each statement of the following five statements. Then write the corresponding answer on the answer book by the title number. You can be gained 3 points for the right choice of per the statement.

(6) The convergence region of

(?x)n?nn?0?

A. ??1,1? B. (?1,1] C. [?1,1) D. ?0,1? (7) If fx(x,y)?2,(1,2). A.

fy(x,y)?3, then f(x,y) does not satisfy at point

?x,y???1,2?df|(1.2)?2dx?3dy B.

fx(x,y)?f?1,2? D.

limfy(x,y)?3

limC. ?x,y???1,2??x,y???1,2?limf(x,y)?f?1,2?

g?x? has local

(8) If f(x) has local maximum and derivative at point 2,

【第 1 页 共 3 页】

maximum and derivative at point 3,the function A. C.

F?x,y??f?x??f?y? holds that

Fx?2,3??0, Fy?2,3??0 B. Fxx?2,3??0 Fyy?2,3??0 D. Fxx?2,3??Fyy?2,3??0

(9) If the general solution of equation then vector= ay''?y'?by?0is y?C1e2x?C2xe2x,

A. ??1/4,1? B. (1/4,1) C. (1/4,?1) D. ??1/4,?1?

1n?x2(2n?1)edx (10) limn??n?0A. exists and equal to 0 B. exists and equal toC. exists and equal to 2 D. does not exist

3. Give the solution of any of in the following problems and write operation

process and answer on the answer book by the title number. You can be gained mark of per problem by the right process and answer. (11) (8pts) Solution the equation. dy+ 3xdx= 3xedx

yn?

（n+1)!+??2?(12) (12pts) Test the convergence of the series ?and find its sum. n2n!0?(13) (8pts) Find

222?z?z, given the equationx+y+z?x?y?xyz.

(14)(10pts)Letz?z?x,y?s?2z?2zsy?esint , satisfy2+2?1, andx?ecostand

?x?y?2z?2z+Compute 22?s?t(x2+y2)1?x2?y2dV, where V is solid in the octant enclosed (15) (10pts) Evaluate???2?x?yD22by the surfacesz?0,x?y?z?2andx?y?1.

(16) (12pts). A firm sells certain commodity on two distinct markets. There two markets have demand functions

p1?7?0.2Q1and p2?5?0.1Q2respectively.

【第 2 页 共 3 页】

The costs of commodity on these markets areC1?3Q1?1 andC2?3Q2?5

separately. If the firm pays tax t per unit commodity, and sells in the same price, then, (1) what is the sales of two markets to maximize firm’s profit? (2) What is the tax rate t to maximize tax income?

(17)(10pts) Ifynsatisfy equationyn+1-0.9yn=xn, then

?n+m+1=0. m?+??mlim【第 3 页 共 3 页】

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