AP Calculus BC Summer Work
Short Answer
1. Decompose
, into partial fractions.
2. Decompose
, into partial fractions.
3. Decompose
, into partial fractions.
4. Graph the point that has polar coordinates
5. Graph the polar equation
.
1
3, 3
6. Find the dis
REVIEW: INTEGRATION BY PARTIAL FRACTIONS, LHOPITALS RULE
AND IMPROPER INTEGRALS
1. Evaluate the limit
a. -1
2. Evaluate
b. 0
3. Evaluate the limit
b.
b. 2
d.
c.
1
16
x2
lim x
x e
.
c. 1
8e x /8 (8 x)
lim
x 0
x2
a.
a. 0
2 x cos 2 x 1
lim
x 0
x2
d. 0
e. No
Name _
AP Calculus BC
Period _
Score _ / 10
HW 8.8 Improper Integrals
For each of the problems below determine whether the integral converges or diverges. For those that
converge, find the limit to which it converges.
1.)
2.)
1
x2 dx
2
3.)
1
1
x
4
dx
3
4
Name _
AP Calculus BC
Period _
Score _ / 10
HW 8.7 Indeterminate Forms and L
Hpitals Rule
Find each limit using LHptials Rule where appropriate.
1.)
3.)
2 x2 x 3
lim
x 1
x 1
x2 x 3
lim
x3
x2
5.)
lim
r 1
7.)
1 r
3
2.)
lim
x3
4.)
lim
x2 x 6
x 3
x 1
x 1
x2 3
Name _
AP Calculus BC
Period _
Score _ / 10
HW 8.6 Integration by Tables
Use the Table of Integrals in Appendix B (Page A20) of your text to answer each of the following. Be sure
to state which formula you are using and identify important values of u, a,
Name _
AP Calculus BC
Period _
Score _ / 10
HW 8.5 Integration by Partial Fractions
1.)
3.)
11x 15
x 2 3x 2 dx
2.)
x
4.)
7 x 25
dx
7x 8
2
5.)
7.)
21
x 2 7 x 10 dx
6.)
x
8.)
2
10 x
dx
9 x 36
9.)
11.)
4 x 15 x 1
x3 2 x 2 5x 6 dx
2
10.)
12.)
3 x 2 22 x
AP CALCULUS - BC
Section Number:
LECTURE NOTES
Topics: Improper Integrals
- Improper Integrals With Infinite Limits of
Integration
8.8
The definition of a definite integral
requires the interval
b
f (x) dx
a, b
MR. RECORD
Day: 1 of 2
to be finite.
a
Fu
AP CALCULUS BC
(Optional Topic)
Section Number:
LECTURE NOTES
MR. RECORD
Topics: Integration by Tables and Other Integration Techniques
Day: 1 of 2
8.6
Integration by Tables
Unfortunately, we are still VERY limited in the number of total functions that we
AP CALCULUS - BC
Section Number:
8.5
LECTURE NOTES
Topics: Partial Fractions
- Linear Factors
MR. RECORD
Day: 1 of 2
Integrals Involving Partial Fraction Decomposition
In this section, youll see a method for rewriting certain rational functions that is ve