Additional Problems
The following problems were taken from Calculus: Early Vectors, by J. Stewart, which is
being used by the other sections of M151.
1. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away
from the wa
M151B Practice Problems for Final Exam
Calculators will not be allowed on the exam. Unjustied answers will not receive credit. On
the exam you will be given the following identities:
n
n(n + 1)
;
k=
2
k =1
n
n(n + 1)(2n + 1)
k=
;
6
k =1
n
2
k3 =
k =1
n(n
M151B Practice Problems for Exam 3
Calculators will not be allowed on the exam. On the exam you will be given the following
identities:
n
n(n + 1)
;
k=
2
k =1
n
n(n + 1)(2n + 1)
k=
;
6
k =1
n
2
k3 =
k =1
n(n + 1)
2
2
.
1. Write down a general expression f
M151B, Fall 2008, Practice Problems for Exam 2
Calculators will not be allowed on the exam.
1. Let
f (x) = cos x sin x,
and compute
3
x
,
4
4
df 1
(1).
dx
2. Show that
1
d
cos1 x =
,
dx
1 x2
1 < x < +1.
3. Let
y = xtan x ,
and compute
0x<
,
2
dy
.
dx
4.
M151B Practice Problems for Exam 1
Calculators will not be allowed on the exam. Unjustied answers will not receive credit.
1. Compute each of the following limits:
1a.
x2 4
.
x 2 x 2
lim
1b.
lim
x 3
x2
1c.
lim
x 0
1d.
lim
x 1
1e.
x
.
2x 3
sin 7x
.
x
x2 +
Additional problems, due Tuesday Nov. 18
1. Use the method of Riemann sums to compute
2
x2 dx.
1
2. Use the method of Riemann sums to compute
1
x3 dx.
0
3. Use the method of Riemann sums to compute
1
ex dx.
0
Hint 1. Use the following summation formula: f
M151B Practice Problems for Final Exam
Calculators will not be allowed on the exam. Unjustied answers will not receive credit. On
the exam you will be given the following identities:
n
n(n + 1)
;
k=
2
k =1
n
n(n + 1)(2n + 1)
k=
;
6
k =1
n
2
k3 =
k =1
n(n
M151B Practice Problems for Exam 3
Calculators will not be allowed on the exam. On the exam you will be given the following
identities:
n
n(n + 1)
;
k=
2
k =1
n
n(n + 1)(2n + 1)
k=
;
6
k =1
n
2
k3 =
k =1
n(n + 1)
2
2
.
1. Write down a general expression f
M151B, Fall 2008, Practice Problems for Exam 2
Calculators will not be allowed on the exam.
1. Let
f (x) = cos x sin x,
and compute
3
x
,
4
4
df 1
(1).
dx
2. Show that
1
d
cos1 x =
,
dx
1 x2
1 < x < +1.
3. Let
y = xtan x ,
and compute
0x<
,
2
dy
.
dx
4.
M151B Practice Problems for Exam 1
Calculators will not be allowed on the exam. Unjustied answers will not receive credit.
1. Compute each of the following limits:
1a.
x2 4
.
x 2 x 2
lim
1b.
lim
x 3
x2
1c.
lim
x 0
1d.
lim
x 1
1e.
x
.
2x 3
sin 7x
.
x
x2 +
Additional problems, due Tuesday Nov. 18
1. Use the method of Riemann sums to compute
2
x2 dx.
1
2. Use the method of Riemann sums to compute
1
x3 dx.
0
3. Use the method of Riemann sums to compute
1
ex dx.
0
Hint 1. Use the following summation formula: f
Additional Problems
The following problems were taken from Calculus: Early Vectors, by J. Stewart, which is
being used by the other sections of M151.
1. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away
from the wa