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64 | P a g e

CHAPTER 7: LIMIT

1. Evaluate the following limits if they exist:

x  1 x  3
3
(a) lim (b) lim
x 1 x  1 x x  9

2. Evaluate the following limits if they exist:

2
 e  1 x  2
3x
(a) lim   (b) lim
x
x 0  e  1  x 3x  6

3. Find the following limits.

x  4  1 1 
2
(a) lim (b) lim   


x 2 x  2 x 0  x 1 x x 

4. Evaluate each of the following limits, if it exists.

x  4 3x  x
4
(a) lim (b) lim
2
x 4 x  2 x x  6

e  e  2x
x
5. Evaluate lim .
x
x 0 e  e  x

6. A function f is defined by
 34 , x   4
 x 
 0 , 2

f ( )   17 , x  4
x
 4 2
 x  3x  4 , x   4, x   3, x  2, x  4
  x  2 x  6
Evaluate lim ( )f x .
x 2
7. Evaluate each of the following limits, if it exists.