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MATH 151 Midterm 1, October 5, 2005, Exams of Calculus

The instructions and questions for a university-level mathematics midterm exam. It covers topics such as limits, derivatives, and velocity. Students are required to provide reasoning for their answers and are not allowed to use graphing calculators.

Typology: Exams

2012/2013

Uploaded on 02/18/2013

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MATH 151
Midterm 1, October 5, 2005
Last Name:
First Name:
SFU Student ID nr:
Section Instructor: N. Bruin / R. Choksi / R. Pyke
1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.
2. Circle your instructor. If you don’t, you lose a mark.
3. This test is comprised of 8 pages.
4. Once the test begins, please check that all pages are intact.
5. Do ALL questions.
6. Clearly explain your answer. No credit will be given for just
writing down the answer.
7. If the answer space provided is not sufficient, write your answer
on the back of the previous page. Clearly mark the question
number.
8. Ordinary Scientific Calculators ONLY are allowed.
NO GRAPHING CALCULATORS ALLOWED.
9. The test is out of 30 points.
10. The duration of the test is 50 minutes.
11. Good luck.
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MATH 151

Midterm 1, October 5, 2005

Last Name:

First Name:

SFU Student ID nr:

Section Instructor: N. Bruin / R. Choksi / R. Pyke

1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.

2. Circle your instructor. If you don’t, you lose a mark.

3. This test is comprised of 8 pages.

4. Once the test begins, please check that all pages are intact.

5. Do ALL questions.

6. Clearly explain your answer. No credit will be given for just

writing down the answer.

7. If the answer space provided is not sufficient, write your answer

on the back of the previous page. Clearly mark the question

number.

8. Ordinary Scientific Calculators ONLY are allowed.

NO GRAPHING CALCULATORS ALLOWED.

9. The test is out of 30 points.

10. The duration of the test is 50 minutes.

11. Good luck.

  1. (4 marks) Evaluate the following limit if it exists. If it does not exist, explain why. You must provide your reasoning which CANNOT be simply “this is what the calculator tells me.”

lim x→ 0 +

x − x √ x

Answer

  1. At time t = 0, a ball is thrown straight up in the air. The height of the ball above the ground at time t seconds is given by the function h(t) (measured in meters) where

h(t) = 20t − 4. 9 t^2.

a) (3 marks) Using any method you like, find an expression for the velocity of the ball at time t.

Answer

b) (2 marks) At what times is the velocity 0?

Answer

Continued on next page

c) (2 marks) What is the maximum height the ball gets above the ground? Clearly explain your answer.

Answer

5a) (1 mark) Find a positive value for δ such that the following statement is true:

If |x| < δ then x^2 < 0 .04.

Answer

b) (1 mark) Write down the precise “  − δ ” definition of

xlim→a f^ (x) =^ L.

Answer

c) (4 marks) Using the definition in part b), prove that

lim x→ 1 (x^2 − 1) = 0.

Answer

Do not write below this line

Question Score Max

Total 30