Math 113 (Calculus II) Final Exam KEY
Short Answer. Fill in the blank with the appropriate answer. 1. (10 points) a. Let y = f (x) for x [a, b] . Give the formula for the length of the curve formed by the
b
graph of this function.
a
1 + (f (x)2 dx
b. Find
Math 113 (Calculus II)
Final Exam Form A KEY
Multiple Choice. In the grid below ll in the correct answer to each question.
1. Here is a series
(1)n
k=1 n(n+1) .
Which of the following is true?
a)
The series diverges by the alternating series test.
b)
The
Math 113 (Calculus II)
Final Exam
Form A KEY
Multiple Choice. Fill in the answer to each problem on your computer-scored answer
sheet. Make sure your name, section and instructor are on that sheet.
1. Find the area of the region bounded by y = e2x , y = e
Math 113 (Calculus II)
Final Exam Form A KEY
Multiple Choice. Fill in the answer to each problem on your scantron. Make sure your
name, section and instructor is on your scantron.
1. Find the area of the region enclosed by y = x and y = 5x x2 .
a)
5
3
b)
Math 113 (Calculus II)
Final Exam Form A KEY
Multiple Choice. Fill in the answer to each problem on your scantron. Make sure your
name, section and instructor is on your scantron.
1. Here is a series
k=1
(1)n
n (n2 + 1)
. Which of the following is true?
a
Math 113 (Calculus II)
Final Exam Form A Fall 2012
RED KEY
Part I: Multiple Choice Mark the correct answer on the bubble sheet provided.
1. Which of the following series converge absolutely?
1)
n=1
(1)n
n2
2)
n=1
(1)n
n
3)
n=1
1
n3
a)
None
b)
1
c)
2
d)
3
Math 113 Fall 2006 Key
Departmental Final Exam
Part I: Short Answer and Multiple Choice Questions
Do not show your work for problem 1.
1. Fill in the blanks with the correct answer.
dx
converge (yes or no) yes
+1
0
cos x
1
dx equals
+C
3
sin x
2 sin2 x
(
Name
KEY
Instructor
Section No.
Student Number
Math 113/113H Winter 2006
Departmental Final Exam
Instructions:
The time limit is 3 hours.
Problems 1-6 short-answer questions, each worth 2 points.
Problems 7 through 13 are multiple choice questions, eac
Math 113 Fall 2005 key
Departmental Final Exam
Part I: Short Answer and Multiple Choice Questions
Do not show your work for problems in this part.
1. Fill in the blanks with the correct answer.
(a) The integral
cos(x + 2) dx equals
(b) The integral
sec x
Math 113 Winter 2007 Key
Departmental Final Exam Part I: Short Answer and Multiple Choice Questions Do not show your work for problems in this part. 1. Fill in the blanks with the correct answer. (a) 1 + x + x2 + is the Maclaurin series for 1 1x
(b)
ln (x