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2017年电大2017年电大《经济数学基础》形成性考核册答案

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2011年电大《经济数学基础》形成性考核册答案

大题必须写步骤,否则0分处理

作业(一)

(一)填空题 1.limx?0x?sinx?___________________.答案:0 x?x2?1,x?02.设f(x)??,在x?0处连续,则k?________.答案:1

?k,x?0?3.曲线y?x+1在(1,2)的切线方程是 .答案:x-2y+1=0

__.答案:2x 4.设函数f(x?1)?x2?2x?5,则f?(x)?__________5.设f(x)?xsinx,则f??()?__________.答案:?π2π 2(二)单项选择题

1.当x→+∞时,下列变量为无穷小量的是( )答案:D

A.

ln(1?x)B.D.x2C.exx?1x2x?1 sinxx2. 下列极限计算正确的是( )答案:B A.limx?0?1 B.lim?x?0xx?1

C.limxsinx?01sinx?1 D.lim?1

x??xx3. 设y?lg2x,则dy?( ).答案:B A.

11ln101dx B.dx C.dx D.dx 2xxln10xx4. 若函数f (x)在点x0处可导,则( )是错误的.答案:B

A.函数f (x)在点x0处有定义 B.limf(x)?A,但A?f(x0)

x?x0 C.函数f (x)在点x0处连续 D.函数f (x)在点x0处可微

1)=x,则f’(x)=( ). 答案:B x1111A.2 B.—2 C. D.—

xxxx5.若f ((三)解答题

1

1.计算极限

x2?3x?21(x?2)(x?1)x?2(1)lim = = ??limlim2x?1x?1x?12x?1(x?1)(x?1)(x?1)x2?5x?61(x?2)(x?3)x?3(2)lim2=lim = lim =

x?2x?6x?8x?2(x?2)(x?4)x?2(x?4)2(1?x?1)(1?x?1)1?x?1lim(3)lim= x?0x?0xx(1?x?1) =limx?0?x?11=lim??

2x(1?x?1)x?0(1?x?1)2?5x2?2 43x23?2x2?3x?5x?lim(4)lim2x??3x?2x?4x??23??x(5)lim5xsin3x33sin3x?lim= x?03xsin5x55x?0sin5xx2?4(x?2)(x?2)(6)lim?lim?4

x?2sin(x?2)x?2sin(x?2)

1?xsin?b,x?0?x?2.设函数f(x)??a,x?0,

?sinxx?0?x?问:(1)当a,b为何值时,f(x)在x?0处有极限存在? (2)当a,b为何值时,f(x)在x?0处连续.

1lim?f(x)?lim?(xsin?b)?bx?0x?0x答案:(1)

sinxlim?f(x)?lim??1x?0x?0x当b?1,a任意时,f(x)在x?0处有极限存在; (2)f(0)= a =limf(0)?b?1

x?0当a?b?1时,f(x)在x?0处连续。

2

3.计算下列函数的导数或微分:

(1) y=x2+2x+log2x-22 求y' 解:y'??x2?'??2x?'??log2x?'??22?'

?2x?2xln2?1 xln2

(2) y=(ax+b)/(cx+d), 求y' 解:y'???ax?b?'?cx?d???ax?b??cx?d?' 2?cx?d?a?cx?d???ax?b?c?cx?d?2?ad?bc?cx?d?2

(3)y?1,求y' 3x?51?2'1313??1???解:y'???3x?5?????3x?5?2??3x?5?'???3x?5?2。

22??

(4)y?x?xex,求y'

1??1xxx2?'??xe?'?x?x'e?x?e?'

2??12解:y'??x???1?1?11?x2??ex?xex??x2?ex?1?x? 22

(5)y=eax sinbx,求dy。

解 y'??eax?'sinbx?eax?sinbx?'?eax?ax?'sinbx?eaxcosbx?bx?'

?aeaxsinbx?beaxcosbx,

3

dy?y'dx?(aeaxsinbx?beaxcosbx)dx

(6)

y?e?xx,求dy

1x'32'1x'11????13?x?2y'?e?x?e?x??????解:

x2??????1x?1x??'11313?x2??exx?2?x2, 22?e?2?(?exdy?y'dx1x31?x2)dx 2

(7)y?cosx?e?x2,求dy。

?x2?x2)'??sinx?(x)'?e???x?'

2解:y'?(cosx)'?(e12??sinx?(x)'?2xe?x21?1?x22??sinx?x?2xe,

21?1?x22dy?y'dx?(?sinx?x?2xe)dx

2

(8)y=sinnx+sin nx,求y'。

解:y'=(sinnx)’+(sin nx)’ =n sinn-1x (sinx)’+cos nx (nx)’

=n cosx sinn-1x +ncos nx

(9)y?lnx?1?x2,求dy。

?? 4

解:y'?1x?1?x2?x?1?x2'??1x?1?x2?1?(1?x)'?

21??12?2?1?x?' ?1?1?x?????x?1?x2?21??12x??1?? 222x?1?x?1?x?1?1x???1???222x?1?x?1?x?x?1?x1?11?x?21?x2?x1?x2

dx1?x2dy?y'dx

(10)y?2。

cot1x1?3x2?2x。 ?,求y'

x?x?12解:因y?2所以y'?2cotcot1x?x21?32?2?2cot1x?x?12?x?2,

161x153cot??1?1?31111???2xln2?cot?'?x2?1??csc?2ln2???'?x2?x6

x?2x6??x?2?56?csc21?2x1cotx1ln2?x?2?x23?2?x 6

1、 下列各方程中y是x的隐函数,试求y'或dy

(1)

x2+y2-xy+3x=1 ,求 dy

解:方程两边对x求导,

2x?2yy'?y?xy'?3?0, (2y?x)y'?y?3?2x,

y'?y?3?2xy?3?2x'dx。 , dy?ydx?2y?x2y?x(2)

sin(x+y)+exy=4x , 求y'

5

2017年电大2017年电大《经济数学基础》形成性考核册答案

2011年电大《经济数学基础》形成性考核册答案大题必须写步骤,否则0分处理作业(一)(一)填空题1.limx?0x?sinx?___________________.答案:0x?x2?1,x?02.设f(x)??,在x?0处连续,则k?________.答案:1?k,x?0?3.曲线y?x+1在(1,2)的切
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