Find the values of a and b so that:
(i) 
may have a finite limit.
(ii) 
= 4
(iii) 
Text Solution
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(i) a = − 
, b = 1
(ii) a = 2, b ∈ R, c = 5, d ∈ R
(iii) a = 3, b = 12, c = 9
Sol. (i) 
= 
= 
Limit exist and have a finite value
So 1 – b = 0 & a + 
= 0
b = 1 , a = 
(ii) 
= 4
⇒ 
= 4
⇒ 
= 4
⇒ a – 2 = 0 & 
⇒ c = 5
⇒ a = 2, c = 5, b ∈ R, d ∈ R
(iii) 
= 2
⇒ 
then a – b + c = 0 .....(1)
2a + b – 2c = 0 .....(2)
3a – 2b + 3c = 12 .....(3)
On solving (1), (2), (3)
we get a = 3, b = 12, c = 9
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