MATH 152-3 Final Examination, Fall 2005, Simon Fraser University, Exams of Calculus

This is a final examination for math 152-3 (calculus 3) at simon fraser university, department of mathematics, held on december 7th, 2005. The exam contains 13 questions covering various topics such as integration, improper integrals, region area, volume of solid of revolution, series, power series, maclaurin series, and complex numbers.

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2012/2013

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Simon Fraser University
Department of Mathematics
Burnaby and Surrey Campus
MATH 152-3, Fall 2005
Final Examination
December 7th, 2005
Last Name (please print): _________________________________________
First Name (please print): _________________________________________
Student Number: _________________________________________
Instructor: B. Kadonoff I. Mercer
Instructions:
1. DO NOT OPEN THIS BOOKLET UNTIL
TOLD TO DO SO.
2. Fill in the above box.
3. This exam contains 15 pages with a total
of 13 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.
Do not write in this table!
Question Marks
1 /24
2 /6
3 /5
4 /9
5 /6
6 /6
7 /6
8 /6
9 /8
10 /6
11 /6
12 /6
13 /6
Total /100
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Simon Fraser University Department of Mathematics Burnaby and Surrey Campus

MATH 152 -3, Fall 2005 Final Examination December 7th, 2005

Last Name (please print): _________________________________________

First Name (please print): _________________________________________

Student Number: _________________________________________

Instructor: B. Kadonoff I. Mercer

Instructions:

  1. DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO.
  2. Fill in the above box.
  3. This exam contains 15 pages with a total of 13 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.

Do not write in this table!

Question Marks 1 / 2 / 3 / 4 / (^5) / 6 / 7 / 8 / 9 / (^10) / 11 / 12 / 13 /

Total /

  1. Evaluate the following: [4 marks each = 24 marks]

a)

2 3

1

∫ x + 9

dx

b)

ln

e x

x dx

e) ∫ x sec( x^2 ) tan( x^2 ) dx

f)

3 1 ( 1)

∫ +

x

x x dx

  1. Determine if the improper integral converges or diverges. Compute

its value if it converges. [6 marks]

( 1) 0

∞ (^) − +

e x dx

  1. Let R be the region bounded by the graphs y =^14 x^2 and x − 2 y + 4 = 0.

[5 marks]

a) Sketch the region R.

b) Find the area R.

  1. Consider the integral

2 0 sin

π

I = ∫ x x dx. Approximate I with n=4 by the

following methods: [3 marks each = 6 marks]

a) Riemann sum with left end-points.

b) Trapezoid rule.

  1. If it takes 200 Newton-metres of work to stretch a certain spring 1 meter beyond its natural length, how much work is required to stretch that same spring ½ meter beyond its natural length? [6 marks]

8. Find the area inside one half of the lemniscate r^2 =cos(2 θ ). [6 marks]

  1. Test the series for convergence or divergence and name the test(s) used. [4 marks each = 8 marks]

a)

3 2 3 0

=

∑ n +

n n

b)

2

1

=

n n n n

  1. Find the Maclaurin series for f ( ) x =cosh x. [6 marks]
  1. Answer the complex number problems below. [6 marks]

a) Write − 3 + i in polar form.

b) Find all the roots of z^4 = − 16.