Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Let f(x) be a bounded function. L 1 = 
(f ′ (x) – λ f(x)) and L 2 = 
f(x) where λ > 0. If L 1 , L 2 both exist and L 1 = L, then prove that L 2 = – 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
L 1 = 
(f ′ (x) – λ f(x)) ⇒ L 1 = 
[As it is a bounded function]
⇒ L 1 = 
⇒ L = L 1 = 
⇒ L = 
⇒ L = 
– λ f(x) ⇒ L = – λ 
f(x)
⇒ L = – λ L 2 ⇒ L 2 = 
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