经济数学基础形成性考核册答案范文模板 25页.docx
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经济数学基础形成性考核册答案范文模板 25页.docx
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经济数学基础形成性考核册答案
篇一:
201X电大《经济数学基础》形成性考核册答案
201X电大《经济数学基础》形成性考核册答案
【经济数学基础】形成性考核册
(一)
一、填空题1.lim
x?
0
x?
sinx
?
___________________.答案:
0x
?
x2?
1,x?
0
2.设f(x)?
?
,在x?
0处连续,则k?
________.答案1
?
k,x?
0?
3.曲线y?
x+1在(1,1)的切线方程是.答案:
y=1/2X+3/2
2
__.答案2x4.设函数f(x?
1)?
x?
2x?
5,则f?
(x)?
__________
5.设f(x)?
xsinx,则f?
?
()?
__________.答案:
?
二、单项选择题
1.当x?
?
?
时,下列变量为无穷小量的是(D)
π2
?
2
?
2sinxx2
A.ln(1?
x)B.C.exD.
xx?
1
1
2.下列极限计算正确的是(B)A.lim
x?
0
xx
?
1B.lim?
x?
0
xx
?
1C.limxsin
x?
0
1sinx
?
1D.lim?
1
x?
?
xx
3.设y?
lg2x,则dy?
(B).A.
11ln101
dxB.dxC.dxD.dx2xxln10xx
4.若函数f(x)在点x0处可导,则(B)是错误的.
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5.若f()?
x,则f?
(x)?
(B).A.
1x
1111
?
?
B.C.D.
xxx2x2
三、解答题1.计算极限
x2?
3x?
2
(1)lim2x?
1x?
1
解:
原式=lim
x?
21?
21(x?
1)(x?
2)
?
?
=lim=
x?
1x?
1x?
1(x?
1)(x?
1)1?
12
x2?
5x?
6
(2)lim2
x?
2x?
6x?
8
解:
原式=lim
x?
32?
31(x?
2)(x?
3)
?
?
=lim
x?
2x?
4x?
2(x?
2)(x?
4)2?
42
(3)lim
x?
0
?
x?
1
x
解:
原式=lim
x?
0
(?
x?
1)(?
x?
1)
x(?
x?
1)
=lim
x?
0
1?
x?
1x(?
x?
1)
=lim?
x?
0
1?
x?
1
=?
12
2x2?
3x?
5
(4)lim2。
x?
?
3x?
2x?
4
352?
?
2
?
2?
0?
0?
2解:
原式=lim
x?
?
3?
?
23?
0?
03xx
sin3x
(5)lim
x?
0sin5x
sin3xsin3x
lim
33x?
0313
解:
原式=lim?
?
?
?
?
?
x?
0sin5xsin5x51555
limx?
05x5x
x2?
4
(6)lim
x?
2sin(x?
2)
解:
原式=lim
(x?
2)(x?
2)x?
2
?
lim(x?
2)?
lim?
4?
1?
4
x?
2x?
2x?
2sin(x?
2)sin(x?
2)
1?
xsin?
b,x?
0?
x?
a,x?
0,2.设函数f(x)?
?
?
sinx
x?
0?
x?
问:
(1)当a,b为何值时,f(x)在x?
0处极限存在?
(2)当a,b为何值时,f(x)在x?
0处连续.解:
(1)因为f(x)在x?
0处有极限存在,则有
xlim?
0?
f(x)?
xlim?
0
?
f(x)又f(x)?
lim(xsi1
xl?
i0
m?
x?
0
?
x
?
b)?
blimf(x)?
lisinx
x?
0
?
x?
0
?
x
?
1即b?
1
所以当a为实数、b?
1时,f(x)在x?
0处极限存在.
(2)因为f(x)在x?
0处连续,则有
xl?
i0
m?
f(x)?
xl?
i0
m?
f(x)?
f(0)又f(0)?
a,结合
(1)可知a?
b?
1所以当a?
b?
1时,f(x)在x?
0处连续.3.计算下列函数的导数或微分:
(1)y?
x2?
2x?
log2x?
22,求y?
解:
y?
?
2x?
2x
ln2?
1
xln2
(2)y?
ax?
b
cx?
d
,求y?
解:
y?
?
(ax?
b)?
(cx?
d)?
(ax?
b)(cx?
d)?
a(cx?
d)?
(ax?
b)c(cx?
d)2=ad?
bc
(cx?
d)2=(cx?
d)
2
(3)y?
13x?
5
,求y?
1
13
解:
y?
?
[(3x?
5)?
2
]?
?
?
1?
2?
12(3x?
5)(3x?
5)?
?
?
32
(3x?
5)?
2(4)y?
x?
xex,求y?
11
解:
y?
?
(x2
)?
?
(xex
)?
?
12
x?
2?
ex?
xex
。
(5)y?
eax
sinbx,求dy解
y?
?
(eax)?
sbx?
eax(
bx)?
?
eax(ax)?
sbx?
eaxcbx(bx)?
aeaxsinbx?
beaxcosbx
=
:
is
dy?
y?
dx?
(aeaxsinbx?
beaxcosbx)dx
1(6)y?
ex
?
xx,求dy
11
313x
1
解:
y?
?
(ex)?
?
(x2)?
?
ex(13
2
?
1x)?
?
2x
?
?
ex
?
32x22
1x
1
dy?
y?
dx?
(?
e3
x
2?
2x2)dx
(7)y?
cosx?
e?
x2
,求dy解:
y?
?
(cosx)?
?
(e?
x2
)?
?
?
sinx(x)?
?
e?
x2
(?
x2)?
?
?
sinx?
x2
2x
?
2xe
(8)y?
sinnx?
sinnx,求y?
解
y?
?
[x)n]?
?
(nx)?
?
n(x)n?
1(x)?
?
cnx(nx)?
?
n(sinx)n?
1cosx?
ncosnx
(9)y?
ln(x?
?
x2),求y?
1解:
y?
?
1x?
?
x
2
(x?
?
x2
)?
?
1(1((1x?
?
x
2
?
?
x2
)2
)?
)
=1
11
?
11xx?
?
x2(1?
2(1?
x)?
2x)?
?
?
x222
1x?
?
x2?
?
x2?
?
x
2(10)y?
2
cot
1x
?
1?
x2?
2x
x
,求y?
35
(2
sin
1x
)?
?
(x?
111解:
y?
?
2
)?
?
(x6
)?
?
(2)?
?
2
sin
x
ln2(sin11?
1?
x)?
?
2x2?
6
x6?
0
si1
i?
3?
1
?
5x
5
?
2
s1x
ln2(1112
6
cosx)(x)?
?
2x
6
x?
2ln21?
31?
x2cosx?
2x2?
6
x64.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:
方程两边同时对x求导得:
:
(s
(x2)?
?
(y2)?
?
(xy)?
?
(3x)?
?
(1)?
2x?
2yy?
?
y?
xy?
?
3?
0y?
?
y?
2x?
3
2y?
x
2y?
x
dy?
y?
dx?
y?
2x?
3dx
(2)sin(x?
y)?
exy?
4x,求y?
解:
方程两边同时对x求导得:
cosx(?
y)?
(x?
y)?
?
exy?
(xy)?
?
4cosx(?
y)?
(1?
y?
)?
exy?
(y?
xy?
)?
4y?
(cos(x?
y)?
xexy)?
4?
cos(x?
y)?
yexy
4?
cos(x?
y)?
yexy
y?
?
xy
cos(x?
y)?
xe
5.求下列函数的二阶导数:
(1)y?
ln(1?
x2),求y?
?
解:
y?
?
12x2
?
(1?
x)?
22
1?
x1?
x
2x2(1?
x2)?
2x(0?
2x)2?
2x2
y?
?
?
()?
?
?
22222
1?
x(1?
x)(1?
x)
(2)y?
1?
xx
,求y?
?
及y?
?
(1)
?
1?
x1?
1?
解:
y?
?
()?
?
(x2)?
?
(x2)?
?
?
x2?
x2
22x
1131
1?
1?
13?
11?
3?
1?
y?
?
?
(?
x2?
x2)?
?
?
?
(?
x2)?
?
(?
)x2?
x2?
x2=1
22222244
315353
《经济数学基础》形成性考核册
(二)
(一)填空题1.若2.
?
f(x)dx?
2x?
2x?
c,则f(x)?
2xln2?
2.
?
(sinx)?
dx
篇二:
经济数学基础形成性考核册答案
电大经济数学基础形成性考核册及参考答案
(一)填空题1.lim
x?
0
x?
sinx
.答案:
0?
___________________
x
x?
0x?
0
,在x
2.设
?
x2?
1,f(x)?
?
?
k,
?
y?
?
0处连续,则k?
________.答案:
1
11x?
22
3.曲线
x在(1,1)的切线方程是答案:
y?
4.设函数5.设
f(x?
1)?
x2?
2x?
5,则f?
(x)?
____________.答案:
2x
ππ
f(x)?
xsinx,则f?
?
()?
__________.答案:
?
22
(二)单项选择题1.函数
y?
x?
1
的连续区间是(D)2
x?
x?
2
A.(?
?
1)?
(1,?
?
)B.(?
?
?
2)?
(?
2,?
?
)
C.(?
?
?
2)?
(?
2,1)?
(1,?
?
)D.(?
?
?
2)?
(?
2,?
?
)或(?
?
1)?
(1,?
?
)2.下列极限计算正确的是(B)
A.lim
xx
x?
0
?
1B.lim?
x?
0
xx
?
1
C.lim3.设y
x?
0
xsin
1sinx?
1D.lim?
1
x?
?
xx
B).
?
lg2x,则dy?
(
A.
11ln101
dxB.dxC.dxD.dx2xxln10xx
f(x)?
A,但A?
f(x0)
4.若函数f(x)在点x0处可导,则(B)是错误的.A.函数f(x)在点x0处有定义B.lim
x?
x0
C.函数f(x)在点x0处连续D.函数f(x)在点x0处可微5.当x
?
0时,下列变量是无穷小量的是(C).
sinxx
A.2B.C.ln(1?
x)D.cosx
x
(三)解答题1.计算极限
x2?
3x?
21
?
?
(1)lim
x?
12x2?
1
1
原式?
lim
(x?
1)(x?
2)x?
1(x?
1)(x?
1)?
lim
x?
2x?
1x?
1?
?
12
(2)limx2?
5x?
61
x?
2x2?
6x?
8?
2
原式=lim
(x-2)(x-3)
x?
2(x-2)(x-4)
?
lim
x?
3x?
2x?
4
?
12
(3)lim
?
x?
1x?
0
x?
?
1
2
原式=lim
(?
x?
1)(?
x?
1)
x?
0
x(?
x?
1)
=lim
?
1
x?
0
?
x?
1
(4)lim
x2?
3x?
5x?
?
3x2?
2x?
4?
1
3
1?
35
原式=
?
2=
13?
33
x?
4x
2
(5)lim
sin3xx?
0sin5x?
3
5
sin3x原式=35lim
x?
0sin5x
=
35
5x
2
=?
12
x2?
4
(6)lim?
4
x?
2sin(x?
2)
原式=lim
x?
2
x?
2
sin(x?
2)x?
2
=4
lim(x?
2)
=
x?
2
sin(x?
2)limx?
2x?
2
2.设函数
1?
xsin?
b,x?
0?
x?
f(x)?
?
a,x?
0,
?
sinx
x?
0?
x?
f(x)在x?
0处有极限存在?
f(x)在x?
0处连续.
x?
0?
问:
(1)当a,b为何值时,
(2)当a,b为何值时,解:
(1)lim?
x
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