Test Total 150 pts
Name
Final Exam
Calculus II
Dec 6, 2010
Dr. Norfolk
Show all work. Partial credit will be given for correct reasoning.
1. Show that f (x) = cos2 x 2x has an inverse g (x) for all x,
Test Total
Name
Exam 1
24 Sept 2010
Calculus II
Dr. Norfolk
For full credit, show your work and use correct notation
1. Let f (x) = tanh(2x).
(a) Show by direct computation that f
ln 2
2
=
3
.
5
4 pts
Name:
Test 3 Calculus II 3450:222
Show all of your work.
April 19, 2013
Dr. Norfolk
1. For each of the following series, determine whether they converge absolutely, converge conditionally, or diverge.
Name:
Test 3 Calculus II 3450:222
Show all of your work.
Nov 12, 2010
Dr. Norfolk
1. For each of the following series, determine whether they converge absolutely, converge conditionally, or diverge. Y
Test Total
Name
Exam 2
13 March 2013
Calculus II
Dr. Norfolk
For full credit, show your work and use correct notation
DO 6 OF THE 8 PROBLEMS
1. Evaluate
1 4x2
dx
x
15 points
2. Evaluate
dx
6x
x2
15 p
Test Total
Name
Exam 1
15 February 2013
Calculus II
Dr. Norfolk
For full credit, show your work and use correct notation
1. Evaluate the following integrals:
(a)
dx
x+3
2 points
(b)
dx
(x 4)3
2 points
Test Total
Name
Exam 2
15 Oct 2010
Calculus II
Dr. Norfolk
For full credit, show your work and use correct notation
Evaluate the following integrals (if possible):
x sec2 2x dx
1.
10 pts
2.
1
x
e
x
dx
Name:
Final Examination Calculus II 3450:222
May 6, 2013
Show all of your work. Give exact values where possible
1. The portion of the disk bounded by y =
the x-axis. Find the volume.
Dr. Norfolk
9 x2
Homework #6
Calculus II 3450:222
Dr. Norfolk
2
1. Determine the number of intervals required to use the Trapezoidal Rule to estimate
sin(x2 ) dx
1
to 6 decimal places (error less than 5 X 107 ).
Answe
Calculus II 3450:222
Homework #9
Dr. Norfolk
1. Consider
(ln(n)2
n2
n=2
(a) Show that the series converges.
Answer: Use the Integral Test.
(b) Find an upper bound for the error in approximating the su
Calculus II 3450:222
(1)n
1. Determine if
n=1
Homework #10
Dr. Norfolk
n2 + 1
converges absolutely, converges conditionally, or diverges.
n3 + 2
Answer: The series converges conditionally, using the L
Homework #8 Calculus II 3450:222
Dr. Norfolk
1. Find the center of mass of a uniform lamina of density , which is bounded by x = 0, x = 1,
y = 0 and y = ex .
Answer:
1 e+1
,
.
e1 4
(1)n n3
2. Determin
Homework #7
Calculus II 3450:222
Dr. Norfolk
1. Find the length of the curve with equation y =
Answer: 6 +
x2 ln(x)
, 2 x 4.
2
4
1
ln(2).
4
2. Find the length of the curve with equation y = ln
Answer:
Homework #5
Calculus II 3450:222
Dr. Norfolk
Evaluate the following integrals:
1.
x sin2 (x) cos(x) dx
Answer:
2.
e
x+7
1
1
x3
sin (x) + cos(x) cos3 (x) + C
3
3
9
dx
Answer: 2( x + 7 1)e x+7 + C
3.
si