College Algebra/Trig Summer Workshop
Limits, Geometric Series,
Partial Fractions, Completing the Square
√
Find lim
x→0
3x + 4 − 2
by using substitution.
x
Use the formula
∞
X
n=0
arn =
∞
X
a
en
to evaluate
1−r
3n+1
n=0
Name:
Find the partial fraction decomposition of
Z
Use the formula
x2
x+4
+ 5x − 6
x
dx
1
=
arctan
+ C to evaluate
x2 + a2
a
a
Z
dx
x2 − 6x + 13
Class Examples
(2x − 1)2 − 9
by using substitution.
x→−1
x+1
a) Find lim
3x2 − 7x + 2
by using substitution.
x→2
2−x
b) Find lim
c) Find lim
x→0
1
5+x
−
1
5
x
d) Use the formula
by using substitution.
∞
X
n=0
arn =
∞
X
a
to evaluate
22n 31−n
1−r
n=0
e) Find the partial fraction decomposition of
Z
f) Use the formula
y
y 2 − 2y − 3
x
dx
1
=
arctan
+ C to evaluate
x2 + a 2
a
a
Z
x2
dx
− 4x + 29
Homework Problems
√
1) Find lim
x→0
16 + x − 4
by using substitution.
x
(x − 3)7 + (x − 3)10
by using substitution.
x→3
4(x − 3)
2) Find lim
3) Use the formula
∞
X
n=0
arn =
∞
X
10n
a
to evaluate
n−1
1−r
n=0 (−9)
4) Find the partial fraction decomposition of
Z
5) Use the formula
x2
5x − 7
− 3x + 2
x
dx
1
=
arctan
+ C to evaluate
x2 + a2
a
a
Z
x2
dx
+ 8x + 25