随堂测试及分析

随堂测试及分析

姓名（Name）

1、

2、Find the following limits

(1)

1

lim

1

x

x

x

→+

(2)

2

1

1

lim

1

x

x

x

→

-

-

(3)

()3

11

lim

h

h

h

→

-+

(4)

2

2

(3)

9

lim

23

x

x

x x

→-

-

+-(5)

2

2

12

lim

12

x

x x

x x

→∞

+-

-+

3、Let ()

()2

303

33

x if x

f x x if x

x if x

⎧-<

⎪⎪

=-≤<

⎨

⎪

->

⎪⎩

(1) Evaluate each limits , if it exists.

(2) Where is f discontinuous?

4、Explain why the function is discontinuous at the givennumber a.

(1) ()

2

2

1

1

1

11

x x

if x

f x a

x

if x

⎧-

≠

⎪

==

-

⎨

⎪=

⎩

(2) ()

212

3

3

3

53

x x

if x

f x a

x

if x

⎧--

≠-

⎪

==-

+

⎨

⎪-=-

⎩

姓名（Name ）

1 Let ()2f x x =，use the definition of derivative to find ()()1,1f f ''-and

()f a '.

2 (a) Find the slope of the tangent line to the curve ()292f x x =- at the point ()2,1.

(b) Find an equation of this tangent line

3 Find equations of the tangent lines to the curve 2

13y x

=

- at the points with x -coordinates 0 and 1-.

4 Use the differentiation rules ()1n n x nx -'

= and ()0C '=to find the following

answers.

(1) ()0.8'= (2) ()π'-=

(3) ()

5

x '

= (4) 1x '⎛⎫= ⎪⎝⎭

(5) '

=

(6) '

=

关于test paper 的说明

为了掌握学生学习情况，本学期在Calculus课堂安排了随堂测验。每月一次测验，时间45分钟，一节课测验，另一节课讲评。

这样的安排能激起学生学习的紧迫感，对留学生学习态度起到一定的促进作用。

这是四月份小测验的成绩对比，左边田芳的试卷是满分，右边李路的试卷是零分。本学期的交换生也参加了测验，她也是满分。