MA 125-5B, Spring 2004

TEST # 1

February 6, 2004 (70 minutes)

Name: SSN:

Max. Points: 100 + 5 Bonus Points: Test Grade:

Turn in all the work which you did to solve the problems, not just the ﬁnal answer.

In particular, include intermediate steps in calculations wherever they are needed.

You may write on the back of a page if you need extra space.

To receive credit, all solutions have to be based on the methods from Chapter 2 of

Stewart’s book.

No book, no notes, and no calculator are to be used!

1. (a) Deﬁne what it means that a function fis continuous at a number a. (3P)

(b) Deﬁne what it means that a function fis diﬀerentiable at a number a. (3P)

2. State the intermediate value theorem. (6P)

3. Find the following limits: (4P+4P+4P+4P)

(a) lim

x→−2

x+ 2

x2−4

(b) lim

x→0

1

cos x

(c) lim

x→∞

2x3−x

1−3x3

(d) lim

x→0

1

x3

4. From the graph of fprovided on the right ﬁnd all numbers asuch that (3P+3P+3P+3P)

(a) lim

x→a+f(x) does not exist

(b) lim

x→a

f(x) does not exist

(c) fis not continuous at a

(d) fis not diﬀerentiable at a

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Subject:
Calculus I

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