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65 | P a g e


 2 x   3x  6 
(a) lim   (b) lim  
x 2 x   2 6x  8  x  x  2 
2

 x  2, x   2
3
  17   2
x
8. Given   x    x  8    A,  2   2
f


x
 Bx  5, 2   5
 10, x  5

(a) Evaluate

x
(i) lim f ( )
x 3 
x
(ii) lim f ( )
x 10 
(b) If lim ( )f x and lim ( )f x exists, find the value of A and B .
x 2 x 5

f   5x 
 
9. (a) If lim  1 , find lim f x .
x 4 x  2 x 4
x  4x  2x  8
2
3
(b) Evaluate lim .
x 4 x  4

 x  3
 x  9 , x  1
2
  , 1 x 


10. Function f is defined as   x   10 px 3
f

2
 x , 3 x  5
 x
 , x  5.
2
 2x  1
(a) Evaluate:
(i) lim f   x (ii) lim f   x (iii) lim f   x .
x 5  x 3 x
 
(b) Find the value of p if lim f x exists.
x 3

11. Evaluate each of the following limits, if exists.