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Let f : R to R be a differentiable fu...

Let f : R `to` R be a differentiable funcation and f (1) = 4 . Then , the value of `lim_(xto1) int_(4)^(f(x))(2t)/( x-1) dt` is

A

8 f' (1)

B

4 f ' (1)

C

2f ' (1)

D

f ' (1)

Text Solution

Verified by Experts

The correct Answer is:
A
`underset( x to 1) (lim) int_(4)^(f(x))(2t)/( x-1)dt = underset( x to1)(lim)(int_(4)^(f(x))2t dt)/( x- 1)` [ using L ' hospital ' s rule]
`=underset(x to1)(lim)( 2f(x)*f ' (x))/(1)=2 f (1)* f' (1)`
= 8 f ' (1)
`[:' f(1) =4]`
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