Limits, Continuity & Differentiability · Limits of indeterminate forms

Let

f : \mathbb{R} \to (0, \infty)

be a twice differentiable function such that

f(3) = 18

f'(3) = 0

and

f''(3) = 4

. Then

\lim_{x\to1}\left(\log_e\left(\dfrac{f(2+x)}{f(3)}\right)^{\frac{18}{(x-1)^2}}\right)

is equal to:

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