Math 136 Exam 1 Practice Problems
1. Find the surface area of the surface of revolution generated by revolving the curve given by
x = 2t2 ln(t), y = 4t, 1 t 4,
around the x-axis?
To solve this we use the equation:
y (t)
SA = 2
2
dx
dt
+
dy
dt
2
dt
In this
Math 136 Winter 2011 Quiz 6
March 2, 2012
Name:
1. For each of the following questions use the vectors v =< 1, 3, 2 >, u =< 2, 1, 4 >, w =< 1, 7 > and
m =< 2, 5 >.
(a) Draw w and m on the same set of 2D axes. Then show using the geometry how to nd m + w
a
Math 136 Winter 2012 Quiz 5
February 22, 2012
Name:
1. (5 Points) Find all values of x for which the following power series converges. Indicate your answer
using interval notation. State all the tests you are using clearly.
k=1
1
k 2 (x 2)k
3k
We use the
Math 136 Winter 2012 Quiz 4
February 13, 2012
Name:
1. (5 Points) Consider the series
2 + 4n
. Does this series converge? Justify your answer completely
(3n 2)2
n=1
using the appropriate test.
First a quick look recognizes that the terms are all positive
Math 136 Winter 2012 Quiz 3
February 6, 2012
Name:
1. (4 Points) Does the sequence bn = e2n ln 1 + 3e2n converge? If so what is the lim bn ? Justify your
n
answer.
Consider,
lim e2x ln 1 +
x
3
e2x
=
=
=
=
=
lim
ln 1 +
1
x
lim
1
3
1+ e2x
lim
both the numer
Math 136 Winter 2012 Quiz 2
January 18, 2012
Name:
1. (4 Points) A isosceles triangular plate with a height of 16 meters and a base width of 10 meters is
suspended vertically in water so that the base of the triangle of the plate is 20meters deep. Find th
Math 136 Winter 2012 Quiz 1
January 9, 2012
Name:
1. Find the length of the curve y = 1 x2
4
1
2
ln(x) for 1 x 2e.
The integral of interest is:
2e
L=
1+
1
2e
2
1
1
x
2
2x
2e
1
1
x+
2
2x
dx =
1
2
dx
2e
1
x2
1
=
+ ln(x)
2e2 + ln(2e)
2
2
2
1
1
1
1
1
12
(2e
Practice from Chapter 13 and 14
1. Given the vectors
u=
v
w
3i + j + 2 k
1
= 2 i + 3 j k
2
= i + 7j + k,
nd the volume of the parallelpiped generated by the three vectors or explain why the three vectors
are co-planar.
The solution can be found by computi
Math 136 Exam 2
February 29, 2012
Name:
1. Please turn o all cell phones and pagers and remove all headphones.
2. There are 6 questions. There should be room to write your solutions on the exam paper. If you need to use
the back sides of pages please do s
Exam 2 Problems
(4x 2)n
, nd the values of x for which this power series converges. Also
n3n
n=0
state clearly what the radius of convergence is.
(1)n
1. Given the series
We start by setting up the Ratio Test:
|4x2|n+1
(n+1)3n+1
lim
n
n |4x2|
n3n
=
=
=
n3
Math 136 Exam 1
January 27, 2012
Name:
1. Please turn o all cell phones and pagers and remove all headphones.
2. There are 6 questions. There should be room to write your solutions on the exam paper. If you need to use
the back sides of pages please do so
Math 136 Fall 2012 Quiz 7
March 12, 2012
Name:
1. Consider the plane passing through the points P = (2, 4, 1), Q = (3, 1, 0) and R = (0, 1, 1).
(a) (4 Points) Find normal vector for this plane.
First we construct two vectors that are in the plane (it does