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

Question

Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow 2}(x-1)^{\frac{1}{3 x-6}} \ & =\lim _{x ightarrow 2}(x-2+1)^{\frac{1}{3(x-2)}}=\lim _{x ightarrow 2}\left\{[1+(x-2)]^{\frac{1}{(x-2)}}ight\}^{\frac{1}{3}}=e^{\frac{1}{3}}\end{aligned}$

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

Solution