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If `f : R to R ` is different function and `f(2) = 6, " then " underset( x to 2) lim underset(6) overset( f(x) (int(2t dt))/(x - 2) ` is

A

24 f' (2)

B

12 f' (2)

C

2 f' (2)

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(x to 2)("lim") int_(6)^(f(X)) (2t)/(x - 2) dt`
Given that f (2) = 6
` = underset(x to 2)("lim") (int_(6)^(f(x)) 2t dt)/((x - 2)) ((0)/(0) "form")`
`underset(x to 2)("lim") (2f (x) f' (x - 0)/(1 - 0)` Using L.H Rule
`= 2 xx 6 f' (2)`
= 12 f' (2)
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