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67 | P a g e

2x  3 x  2 1
16. (a) Evaluate lim .
3
x 2x  1
(b) Determine the values of A and B if the limit of ( )f x exist at the points x   1 and

x  4.

 4 , x   1


4

f   x   Ax B ,  1 x 
 2
 Ax  Bx  1 , x  4
2  x
17. (a) Evaluate lim .

x 4 4 x

2
(b) If lim ( )f x  and lim ( ) 64g x  , find lim f ( ) x g ( )  x  ( )f x   .
2
x 1 x 1 x 1
18. Function f is defined as
 x  2 p , x  1


 q , 1 x  2
2
( )f x   x  4 , 2  x  6

 x  2
 2x  2 x  2
 , x  6
x   2 3x  1

(a) Find lim f ( ).
x
x
(b) Find the value of p if lim ( ) 5f x  .
x 2
(c) Find the value of q if lim ( )f x exists
x 2
19. Evaluate each of the following limits, if exists.
2
2x  6 3x  11x   1
3
x
(a) lim (b) lim
x 3 x  2 2x  3 x 4x  2x 3

 ax  7, x   k
 3,   
 k x 1


2
20. Given   x   x  1, 1 x  k .
f
 3x  1, k   5
x

 16, x  5

 
Find the values of k if lim f x exists.
x k