lim _{x rightarrow 2}(x-1)^{frac{1}{3x-6}} = | vedclass

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Question

(C) Let $L = \lim _{x \rightarrow 2}(x-1)^{\frac{1}{3x-6}}$.Since the form is $1^{\infty}$,we use the formula $\lim _{x \rightarrow a} f(x)^{g(x)} = e

Vedclass · Accepted Answer

$e^{\frac{1}{3}}$

Vedclass · Answer

(C) Let $L = \lim _{x \rightarrow 2}(x-1)^{\frac{1}{3x-6}}$.Since the form is $1^{\infty}$,we use the formula $\lim _{x \rightarrow a} f(x)^{g(x)} = e^{\lim _{x \rightarrow a} g(x)(f(x)-1)}$.Here,$f(x) = x-1$ and $g(x) = \frac{1}{3x-6}$.$L = e^{\lim _{x \rightarrow 2} \frac{1}{3(x-2)} (x-1-1)}$.$L = e^{\lim _{x \rightarrow 2} \frac{x-2}{3(x-2)}}$.$L = e^{\lim _{x \rightarrow 2} \frac{1}{3}} = e^{\frac{1}{3}}$.

$\lim _{x \rightarrow 2}(x-1)^{\frac{1}{3x-6}} = $

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