Continuous Function - Calculus I - Exam, Exams for Calculus I. Birla Institute of Technology and Science

Calculus I

Description: Continuous Function, Differentiable Function, Intermediate Value Theorem, Find Following Limits, Equation for Tangent Line, Position of Vehicle, Acceleration of Vehicle, Concave Downwards are some points from this exam paper of Calculus I.
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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
x24
(b) lim
x0
1
cos x
(c) lim
x→∞
2x3x
13x3
(d) lim
x0
1
x3
4. From the graph of fprovided on the right find all numbers asuch that (3P+3P+3P+3P)
(a) lim
xa+f(x) does not exist
(b) lim
xa
f(x) does not exist
(c) fis not continuous at a
(d) fis not differentiable at a
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