Math 262
Exam 4 - Practice Problem Solutions
1. For each of the following sequences, determine whether the sequence converges or diverges. If a sequence converges,
whenever possible, nd the value of the limit of the sequence.
(a)
n+2
3n 1
Notice that lim
Math 262
Exam 2 - Practice Problems
1. Determine whether or not each of the following functions is one-to-one.
(a) f (x) = ln(x2 )
Notice that f (2) = f (2) = ln 4. Therefore, this function is not one-to-one.
(b) f (x) = x5 + 2x3 2
First notice that f is
Math 262
Exam 1 - Practice Problems
1. Find the area between the given curves:
(a) y = x2 + 1 and y = 3x 1
(b) y = x2 1 and y = 1 x on [0, 2]
(c) y = x, y = 2, y + x = 6, and y = 0
(d) x = y 2 , x = 4
2. A pottery jar has circular cross sections or radius
Math 262
Exam 1 - Practice Problems
1. Find the area between the given curves:
(a) y = x2 + 1 and y = 3x 1
First notice that these curves intersect when x2 +1 = 3x1, or when x2 3x+2 = 0. That is, when (x2)(x1) = 0,
or when x = 2 and x = 1.
Next, notice th
Math 262
Exam 2
Name:
Instructions: You will have 60 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem will be proportional to the amount of correct work shown. Answers w
Math 262
Exam 3 - Version 1
Name:
Instructions: You will have 60 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem will be proportional to the amount of correct work show
Math 262
Exam 2 - Practice Problems
1. Determine whether or not each of the following functions is one-to-one.
(a) f (x) = ln(x2 )
(b) f (x) = x5 + 2x3 2
2. Determine whether or not each of the following functions is one-to-one. If it is, nd the inverse f
Math 262
Exam 3
Practice Problem Solutions
1. Evaluate the following integrals:
sec3 x tan3 x dx
(a)
=
tan2 x sec2 x sec x tan x dx =
(sec2 x 1) sec2 x sec x tan x dx
Let u = sec x. Then du = sec x tan x dx, and we have
(u2 1)u2 du =
u4 u2 du
1
1
15 13
u
Math 262
Quiz 1
Due: 09/09/2009
Name:
This is a Take-Home Quiz. You may use your book and course notes, and you may consult with other
members of the class, but you may not consult with outside tutors (at least not on these specic problems).
2
1. (5 point
Math 262
Quiz 1
Solutions
Name:
This is a Take-Home Quiz. You may use your book and course notes, and you may consult with other
members of the class, but you may not consult with outside tutors (at least not on these specic problems).
2
1. (5 points) Fin
Math 262
Exam 4 - Practice Problems
1. For each of the following sequences, determine whether the sequence converges or diverges. If a sequence converges,
whenever possible, nd the value of the limit of the sequence.
(a)
n+2
3n 1
(b)
(1)
(c)
nen
cos n
en
Math 262
Exam 1 Solutions
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem will be proportional to the amount of correct work shown. Answe