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Question:

Let f: R→R be a continuously differentiable function given that f(2)=6 and f'(2)=148. If ∫₆ˣ f(t)⁴t³dt=(x-2)g(x), then limₓ→₂g(x) is equal to?

12

24

36

18

Solution:

Correct option is D. 18
limₓ→₂g(x) = limₓ→₂ ∫₆ˣ f(t)⁴t³/(x-2)dt;
= limₓ→₂ [4f³(x)f'(x)]/1
= 4f³(2)f'(2) = 4(6)³(148) = 18.