Published by:
CGP EDU Academic Team
Published on: August 12, 2026
(i)If f(x) = 
, evaluate 
f(x).
(ii)Let f(x) = 
, if 
f(x) exist, then find value of λ .
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(i)Limit does not exist
(ii) λ = –2
Sol. (i) If f(x) = 
⇒ 
f(x) exist if L.H.L. = R.H.L.
R.H.L. = 
f(x) = 
(2x – 3) = 
[2(1 + h) – 3] = – 1
L.H.L. = 
f(x) = 
(x + 1) = 2
L.H.L. ≠ R.H.L.
so limit does not exist at x = 1
(ii) 
f(x) exist if R.H.L. = L.H.L.
so 
(2x – 3) = 
(x + λ ) ⇒ 2 – 3 = 1 + λ ⇒ λ = – 2
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