Published by:
CGP EDU Academic Team
Published on: August 12, 2026
(i)Show that 
for some c ∈ (0, 2)
(ii) f(x) is a continuous function x ∈ R, then show that 
some α ∈ (1, 2)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(i)By mean value theorem for a cont. function 
= f(c)(b – a) for some c ∈ (a, b)
Hence 
= sinc cos 
(2 – 0) for some c ∈ (0, 2).
(ii) Ι = 
, let x = t 2 ; Ι = 
= 2 α f( α 2 )(2 – 1) for some α ∈ (1, 2)
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