《经济数学基础12》形成性考核册及参考答案(一)填空题
作业(一)
C.limxsinx?01sinx?1 D.lim?1
x??xxx?sinx?___________________1.limx?0x2.设
3. 设y,则dy?( ).答案:B ?lg2x.答案:0
A.
?x2?1,x?0,在x?0处连续,则k?________.答案:1 f(x)???k,x?0?y?x在(1,1)的切线方程是 .答案:y?11x? 2211ln101dx B.dx C.dx D.dx 2xxln10xxf(x)?A,但A?f(x0)
4. 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.limx?x03.曲线
C.函数f (x)在点x0处连续 D.函数f (x)在点x0处可微 5.当x4.设函数5.设
__.答案:2x f(x?1)?x2?2x?5,则f?(x)?__________.答案:?πf(x)?xsinx,则f??()?__________2y?x?1x2?x?2π 2?0时,下列变量是无穷小量的是( ). 答案:C
sinxx1?x) D.cosx A.2 B. C.ln(x(三)解答题 1.计算极限
(二)单项选择题 1. 函数
的连续区间是( )答案:D
A.(??,1)?(1,??) B.(??,?2)?(?2,??) C.
x2?3x?21x2?5x?61?? (2)lim2? (1)lim2x?1x?22x?1x?6x?82x2?3x?511?x?11? ?? (4)lim2(3)limx??x?0x23x?2x?43sin3x3x2?4? (6)lim(5)lim?4
x?0sin5xx?25sin(x?2)(??,?2)?(?2,1)?(1,??) D.
(??,?2)?(?2,??)或
(??,1)?(1,??)
2. 下列极限计算正确的是( )答案:B A.limx?0xx?1 B.lim?x?0xx?1
1
??xsin1?b,x?02.设函数
f(x)??x?a,x?0,
??sinx?xx?0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.
答案:(1)当b?1,a任意时,f(x)在x?0处有极限存在;(2)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?
答案:
y??2x?2xln2?1xln2 (2)y?ax?bcx?d,求y?
答案:y??ad?cb(cx?d)2
(3)
y?13x?5,求
y?
答案:
y???32(3x?5)3
(4)
y?x?xex,求y?
答案:
y??12x?(x?1)ex
(5)
y?eaxsinbx,求dy
答案:dy?eax(asinbx?bcosbx)dx1(6)
y?ex?xx,求dy
1答案:dy?(12x?1x2ex)dx (7)
y?cosx?e?x2,求dy
答案:dy?(2xe?x2?sinx2x)dx
(8)
y?sinnx?sinnx,求y? 答案:
y??n(sinn?1xcosx?cosnx)
2
(9)
y?ln(x?1?x2),求y? 答案:y??1
1?x2cot13(10)
y?2x?1?x2?2xx,求
y?
1x答案:y??2cotln21?3521x2sin1?2x?6x?6 x4.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
答案:dy?y?3?2x2y?xdx (2)sin(x?y)?exy?4x,求y?
答案:y??4?yexy?cos(x?y)xexy?cos(x?y) 5.求下列函数的二阶导数: (1)
y?ln(1?x2),求y??
??2?2x2答案:y?(1?x2)2
(2)
y?1?xx,求
y??及y??(1)
5???34x?32?14x?答案:y2,y??(1)?1
作业(二)
(一)填空题 1.若
?f(x)dx?2x?2x?c,则f(x)?__________________.答案:
_2xln2?2
2.
?(sinx)?dx?________.答案:sinx?c 3. 若
?f(x)dx?F(x)?c,则?xf(1?x2)dx? .答案:
?12F(1?x2)?c 4.设函数dedx?1ln(1?x2)dx?___________.答案:0 5. 若P(x)??01x1?t2dt,则P?(x)?__________.答案:?11?x2
(二)单项选择题
3
1. 下列函数中,( )是xsinx的原函数. A.
2
(三)解答题
1cosx2 B.2cosx2 C.-2cosx2 D.-
1cosx2
1.计算下列不定积分
22答案:D
2. 下列等式成立的是( ). A.sinxdx?d(cosx) B.lnxdx?d(1x)
C.2xdx?1ln2d(2x) D.1xdx?dx 答案:C
3. 下列不定积分中,常用分部积分法计算的是( ). A.?cos(2x?1)dx, B.?x1?x2dx C.
?xsin2xdxD.
?x1?x2dx
答案:C
4. 下列定积分计算正确的是( ). A.
?1?12xdx?2 B.?16?1dx?15
C.??3???(x2?x)dx?0 D.???sinxdx?0
答案:D
5. 下列无穷积分中收敛的是( ). ??1xdx??A.
?1 B.?1??x??1x2dx C.?0edx D.?1sinxdx 答案:B
1)?3x(exdx
3x答案:
ex?c ln3e(2)
?(1?x)2xdx
答案:2x?43253x2?5x2?c(3)?x2?4x?2dx 答案:
12x2?2x?c (4)?11?2xdx 答案:?12ln1?2x?c
4
(5)
?x2?x2dx
答案:1323(2?x)2?c
(6)
?sinxxdx
答案:?2cosx?c
(7)
?xsinx2dx 答案:?2xcosx2?4sinx2?c(8)
?ln(x?1)dx
答案:(x?1)ln(x?1)?x?c 2.计算下列定积分 (1)
?2?11?xdx
答案:
52
12x(2)
?e1x2dx 答案:e?e
(3)
?e311x1?lnxdx
答案:2
?(4)
?20xcos2xdx 答案:?12 (5)
?e1xlnxdx
答案:14(e2?1) (6)
?40(1?xe?x)dx
答案:5?5e?4
作业三 (一)填空题
?101.设矩阵A??4?3?23??216答案:3
5
?5?2??,
则A的元素a23?__________________.?1??