Calculus AB
Limit Review
1.
a) lim x
 f(x) b) lim x

1 c) lim x

1
 d) lim x

1
 e) lim x

1
2.
The following problems are very easy…try them.
3
Name _______________________________
3.
What was the “big idea” behind all of the above limit problems? Describe in your own words, using complete sentences, why they are so easy to evaluate.
4.
What does
7
0 a) 7
= ? b) 0 c) Undefined d) Any number e) None of these
5.
What does
0
0 a) 1
= ? b) 0 c) Undefined d) Any number e) None of these

6.
Try to evaluate the following limits using direct substitution. Observe what happens. a) lim x

2 x
2 
5 x

4 x
2 
2 x

8 b) lim x

4 x
2 
5 x

4 x
2 
2 x

8 c) Find the vertical asymptotes and holes of
 x
2 
5 x

4
without a calculator. There can be x 2 
2 x

8 more than one answer!
A. Vertical Asymptote at x = 4
B. Vertical Asymptote at x = –2
C. Hole at x = –2
D. Hole at x = 4
E. None of these x
2 
5 x

4 d) Graph
 x
2 
2 x

8
without a calculator. e) Discuss the limit below graphically. lim x

2 x
2 
5 x

4 x
2 
2 x

8 f) Discuss the limit below graphically. lim x

4 x
2 
5 x

4 x
2 
2 x

8 g) Write a sentence explaining how the limits you found graphically in parts e) and f) connect to those you tried to find by direct substitution in parts a) and b).

Take a minute to process the following ideas:
More Practice! First, try to evaluate each of the following using direct substitution. Then, use algebra to evaluate the limits. x
2  
6
7.
lim x

3 x

3 x
8.
lim x

0 x
9.
lim x

0
 x
1
 

1
2 2 x
10.
lim x 0
 x
  x

2  x
2
 x