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. You must state which test(s) you are using, and show t
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, and nd g
1
.
2
2
10 points
2
3(2x ) 9x3 + 4
2. Use log
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. You must state which test(s) you are using, and show tha
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 points
1
3. Evaluate
(ex
ex
dx
2)(e2x + 4)
15 points
4.
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
(c)
x2
x
dx
+ 17
2 points
(d)
dx
x2 + 19
2 points
(e)
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
10 pts
Page 1 Total (20 points)
1
3.
x2
dx
4x + 3
10
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 , y = 0, x = 0 and x = 1 is rotated about
10 points
2.
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 ).
Answer: It suces that n 1733.
Hint: With f (x) = sin(x2 ), w
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 sum S by the partial sum SN .
(ln(N )2 + 2 ln(N ) + 2
Ans
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 Limit Comparison Test, and Alternating
Series Test.
n
7n
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. Determine if the sequence cfw_an , where an = 3
, converges. If
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: ln
ex + 1
, 0 < a x b.
ex 1
sinh(b)
sinh(a)
e2x + 1
Hi
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
(b) Find the exact value of (f (1) )
3
.
5
4 pts
2. Ev