Midterm 2 Exam for MATH 157-3 at Simon Fraser University, Summer 2008, Exams of Calculus

A midterm exam for the math 157-3 course at simon fraser university, held on july 2nd, 2008. The exam contains 5 questions worth a total of 40 marks, covering topics such as elasticity of demand, derivatives, and approximations. Students were required to show all their work and only scientific calculators were allowed.

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2012/2013

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Simon Fraser University
Department of Mathematics
Burnaby Campus
MATH 157-3, Summer 2008
Midterm 2
July 2nd, 2008, 11:30 – 12:20
Last Name (please print): _________________________________________
First Name (please print): _________________________________________
Student Number: _________________________________________
Instructor: P. Menz
Instructions:
1. DO NOT OPEN THIS BOOKLET UNTIL
TOLD TO DO SO.
2. Fill in the above box.
3. This exam contains 7 pages with a total of
5 questions. Once the exam begins please
check to make sure your exam is
complete.
4. SHOW ALL YOUR WORK!
5. If you run out of space in a problem, use
the space on the back of the previous page
and clearly indicate where the solution
continues.
6. Only scientific, non-programmable
calculators with no differentiation and
integration capabilities are allowed.
7. No book, paper, or device, other than the
usual writing instruments, this booklet and
an acceptable calculator, shall be within
reach of a student during the examination.
8. During the examination, speaking to,
communicating with, or deliberately
exposing written papers to the view of
other examinees is forbidden.
9. Try your Best!
Do not write in this table!
Question Marks
1 /7
2 + /12
3 /4
4 /7
5 /10
Total /40
pf3
pf4
pf5

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Simon Fraser University

Department of Mathematics

Burnaby Campus

MATH 157-3, Summer 2008

Midterm 2

July 2

nd , 2008, 11:30 – 12:

Last Name (please print): _________________________________________

First Name (please print): _________________________________________

Student Number: _________________________________________

Instructor: P. Menz

Instructions:

  1. DO NOT OPEN THIS BOOKLET UNTIL

TOLD TO DO SO.

  1. Fill in the above box.
  2. This exam contains 7 pages with a total of

5 questions. Once the exam begins please check to make sure your exam is complete.

  1. SHOW ALL YOUR WORK!
  2. If you run out of space in a problem, use

the space on the back of the previous page and clearly indicate where the solution continues.

  1. Only scientific, non-programmable

calculators with no differentiation and integration capabilities are allowed.

  1. No book, paper, or device, other than the

usual writing instruments, this booklet and an acceptable calculator, shall be within reach of a student during the examination.

  1. During the examination, speaking to,

communicating with, or deliberately

exposing written papers to the view of other examinees is forbidden.

  1. Try your Best!

Do not write in this table!

Question Marks

Total /

  1. Suppose the demand function for a certain product is given by.

This equation tells us the price that must be charged per unit to sustain a

demand of x units.

2 p = 4000 − 5 x

a) Write down the formula for the elasticity of demand E. [1 mark]

b) Find the elasticity of demand E as a function of x. [3 marks]

c) Find and interpret the elasticity of demand when x = 20. [3 marks]

c) g x ( ) = tan x , g ′′( ) x

d) ( )

4 sin y = cos x ,^

dy

dx

  1. You are given the graphs of two functions y = f ( ) x and y = g x ( )defined for

all real numbers. Below are 4 further graphs. Identify those graphs that are the

first derivative of f and g respectively and label the curves by placing f ′( ) x and

g ′( ) x into the appropriate box. [4 marks]

  1. A certain property in Vancouver grows exponentially from being valued at

$250,000 in the year 2000 to $400,000 in the year 2006. Let t measure time in

years with t = 0 meaning year 2000. [10 marks]

a) Write an exponential function that models this.

b) What will be the approximate value of the property in 2010?