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

Question

Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow 1} \frac{2^{2 x-2}-2^x+1}{\sin ^2(x-1)}=\lim _{x ightarrow 1} \frac{\left(2^{x-1}-1ight)^2}{\sin ^2(x-1)}=\lim _{x ightarrow 1} \frac{\frac{\left(2^{x-1}-1ight)^2}{(x-1)^2}}{\frac{\sin ^2(x-1)}{(x-1)^2}} \ & =\frac{(\log 2)^2}{1^2}=(\log 2)^2\end{aligned}$

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

Solution