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x  1 1 x  2 4x  5

(a) lim . (b) lim .
x 2 x  2 x 1 x  1


 2x  4, x k
12. (a) Given   x  
f

k
 kx  5 , x k .
 
Find the value of k  if lim f x exist.
0
x k

f
(b) The function   x is defined as:
 x , x  1



f   x   x  1, 1 x  3


x
 8 2 , 3 x 6

  4 , x  6.
Find
(i) lim f   x (ii) lim f   x (iii) lim f   x
x 1 x x 3

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

16x  4 x  7
2
(a) lim (b) lim
2

x 4x  3 x 7 3x  4 5


 a x , x   b
 1


14. Given   x   x  6 ,   x b
b
f
 3

  x  5a , x b

 
 
Find the values of constants a and b if lim f x and lim f x exist.
x b x b

x  25
2
15. Evaluate lim .

x 5 2x  1 3