17春秋华师《高等数学(文)》在线作业

17春秋华师《高等数学(文)》在线作业
17春秋华师《高等数学(文)》在线作业

华师《高等数学(文)》在线作业

一、单选题(共20 道试题,共40 分。)

1. 下列函数在点x=0处连续但不可导的是( )。

A. 1/x

B. |x|

C. x^2

D. lnx

正确答案:

2. 曲线y=xlnx的平行于直线x-y+1=0的切线方程为()

A. y=x-1

B. y=-(x+1)

C. y=(lnx-1)(x-1)

D. y=x

正确答案:

3. 下列各微分方程中为一阶线性方程的是()。

A. xy'+y^2=x

B. y'+xy=sinx

C. yy'=x

D. y'^2+xy=0

正确答案:

4. 若f(x)是奇函数,g(x)是偶函数,且f[g(x)]有意义,则f[g(x)]是()

A. 偶函数

B. 奇函数

C. 非奇非偶函数

D. 偶函数或奇函数

正确答案:

5. 点x=0是函数y=x4的

A. 驻点但非极值点

B. 拐点

C. 驻点且是拐点

D. 驻点且是极值点

正确答案:

6. 若f(x)是奇函数,且对任意的x,有f(x+2)=f(x),则f(1)=()

A. -1

B. 0

C. 1

D. 2

正确答案:

7. y=xsin3x,则dy=()

A. (-cos3x+3sin3x)dx

B. (sin3x+3xcos3x)dx

C. (cos3x+sin3x)dx

D. (sin3x+xcos3x)dx

正确答案:

8. 当x→0时,ln(1+x)与x比较是()。

A. 高阶无穷小量

B. 等价无穷小量

C. 非等价的同阶无穷小量

D. 低阶无穷小量

正确答案:

9. 下列微分方程中,属于变量可分离的微分方程是()。

A. xsin(xy)dx+ydy=0

B. y'=ln(x+y)

C. y'=xsiny

D. y'+y/x=e^x*y^2

正确答案:

10. 若f(x)在区间(-∞,+∞)内是单调增加,g(x)是单调减少,则f[g(x)]在-∞,+∞)内是()

A. 单调增加

B. 单调减少

C. 不是单调函数

D. 无法判定单调性

正确答案:

11. 已知y= 4x3-5x2+3x-2, 则x=0时的二阶导数y"= ( )

A. 0

B. 10

C. 1

D. -10

正确答案:

12. 函数y=x/(x+1)的水平渐近线为()。

A. y=-1

B. y=0

C. y=1

D. y=2

正确答案:

13. 设函数f(x)=|x|,则函数在点x=0处()

A. 连续且可导

B. 连续且可微

C. 连续不可导

D. 不连续不可微

正确答案:

14. 函数f(x)=tanx能取最小最大值的区间是()。

A. [0,π]

B. (0,π)

C. [-π/4,π/4]

D. (-π/4,π/4)

正确答案:

15. 若f(x)在[a,b]上连续的函数,则f(a)f(b)<0是f(x)在(a,b)内取零值的()。

A. 充分条件

B. 必要条件

C. 充要条件

D. 无关条件

正确答案:

16. 函数f(x)在区间[a,b]上连续是函数f(x)在区间[a,b]上可积的()

A. 充分条件

B. 必要条件

C. 充分必要条件

D. 既非充分又非必要条件

正确答案:

17. 若f(x)是奇函数,g(x)是偶函数,且f[g(x)]有意义,则f[g(x)]是()。

A. 偶函数

B. 奇函数

C. 非奇非偶函数

D. 偶函数或奇函数

正确答案:

18. 设x和y分别是同一变化中的两个无穷大量,则x-y是()。

A. 无穷大量

B. 无穷小量

C. 常数

D. 不能确定

正确答案:

19. 设f(x)和g(x)都是递增函数,则下列函数为递增函数的是()。

A. f(x)+g(x)

B. f(x)-g(x)

C. f(x)*g(x)

D. |f(x)*g(x)|

正确答案:

20. x→1时,sin(x-1)/(1-x2)的极限是()

A. 1

B. 0

C. -1/2

D. 1/2

正确答案:

华师《高等数学(文)》在线作业

二、多选题(共20 道试题,共40 分。)

1. 下列说法不正确的是()

A. 无穷小的和仍为无穷小

B. 无穷大的和仍为无穷大

C. 有界函数与无穷大的乘积仍为无穷大

D. 收敛数列必有界

正确答案:

2. 下列命题正确的是()

A. 两个偶函数之和是偶函数

B. 两个奇函数之和是奇函数

C. 两个偶函数之积是偶函数

D. 两个奇函数之积是偶函数

正确答案:

3. 下列函数是基本初等函数的是()

A. y=C

B. y=sinx

C. y=tanx

D. y=sin2x

正确答案:

4. 下列哪个函数的导数为零()

A. cos3x

B. sine

C. sinx

D. tan2

正确答案:

5. 若函数f(x)的二阶导数是ex,下列哪些可能是函数f(x)

A. exp(x-2)

B. exp(x)+x

C. exp(x)

D. exp(x)+e*e

正确答案:

6. 下列结论正确的是()

A. 不定积分的导数等于被积函数

B. 不定积分的微分等于被积表达式

C. 有限个函数的代数和的不定积分,等于各个函数的不定积分的代数和

D. 被积函数中的常数因子,可以提到积分符号外面来

正确答案:

7. 下列公式正确的是()

A. dx=1/7d(7x-3)

B. xdx=1/10d(5x*x)

C. dx=-1d(1-x)

D. 1/xdx=-1/3d(5-3lnx)

正确答案:

8. 下列哪些函数是周期函数()

A. y=cos2x

B. y=sin(x/2)

C. y=xcosx

D. y=sinx

正确答案:

9. 下列结论正确的是()

A. 两个函数的和的导数等于两个函数导数的和

B. 两个函数的差的导数等于两个函数导数的差

C. 反函数的导数等于原来函数导数的倒数

D. 两个函数的积的导数等于第一个函数的导数乘以第二个函数,再加上第一个函数乘以第二个函数的导数

正确答案:

10. 下列结论正确的是()

A. 两个无穷小的积仍为无穷小

B. 两个无穷小的商仍为无穷小

C. 有界函数与无穷小的乘积仍为无穷小

D. 在同一变化过程中,无穷大的倒数为无穷小

正确答案:

11. 下列哪些函数是非周期函数()

A. sin(1/x)

B. cos(1/x)

C. sinx*sinx

D. tanx

正确答案:

12. 下列公式正确的是()

A. (lnx)'=1/x

B. (sinx)'=cosx

C. (cosx)'=sinx

D. (secx)'=secxtanx

正确答案:

13. 曲线y=lnx/x的渐进线为()

A. y=0

B. y=1

C. x=1

D. x=0

正确答案:

14. 下列结论正确的是()

A. 函数代数和的定积分等于每个函数定积分的代数和

B. 常数因子可以提到积分号外面

C. 定积分的上、下限相等时,定积分值等于零

D. 定积分上、下限对调后,定积分改变符号

正确答案:

15. 下列求导公式正确的是()

A. (xsinx+cosx)'=xcosx

B. (sinx/(1+cosx))'=1/(1+cosx)

C. (ln(tanx))'=2/sin2x

D. (ln(lnx))'=1/xlnx

正确答案:

16. 若函数f(x)的微分是cos2xdx,下列哪些函数可能是f(x)()

A. sinxcosx

B. sinxcosx+2

C. 1/2sin2x

D. 1/2sin2x

正确答案:

17. 若果∫df(x)=∫dg(x),则必有()

A. f'(x)=g'(x)

B. df(x)=dg(x)

C. f(x)=g(x)

D. d[∫f'(x)dx]=[∫g'(x)dx]

正确答案:

18. 下列各函数在[1,e]上不满足拉格朗日中值定理条件的是()

A. y=ln(lnx)

B. y=lnx

C. y=1/lnx

D. y=ln(2-x)

正确答案:

19. 下列函数中,奇函数是()

A. y=x5+sinx

B. y=sinx+2cosx

C. y=x2sinx

D. y=x(x-1)(x+1)

正确答案:

20. 函数f(x)的导数f'(0)=1,则f(x)可能是()

A. sinx

B. ln(x+1)

C. x-1

D. arctanx

正确答案:

华师《高等数学(文)》在线作业

三、判断题(共10 道试题,共20 分。)

1. 函数y=sinx+x^2是周期函数。

A. 错误

B. 正确

正确答案:

2. 在自变量的同一变化过程中,如果f(x)为无穷小,则1/f(x)无穷大

A. 错误

B. 正确

正确答案:

3. 函数可积与函数可导之间既非充分也非必要条件

A. 错误

B. 正确

正确答案:

4. 函数在f(x)在x0处有定义,是当x→x0时f(x)有极限的充分必要条件。

A. 错误

B. 正确

正确答案:

5. 微分运算与求不定积分的运算是互逆的

A. 错误

B. 正确

正确答案:

6. 函数f(x)=1/x在(0,+∞)是减函数。

A. 错误

B. 正确

正确答案:

7. 函数y=sinx在其定义域内有界

A. 错误

B. 正确

正确答案:

8. 被积函数为1的定积分等于上限减去下限的值

A. 错误

B. 正确

正确答案:

9. 设x1,x2分别是函数f(x)的极大值点和极小值点,则必有f(x1)>f(x2)

A. 错误

B. 正确

正确答案:

10. 函数在某点可导的充要条件是函数在该点的左右导数存在且相等

A. 错误

B. 正确

正确答案:

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