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$$
\lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right)
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\lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right)
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1155 Upvotes
Verified Answer
The correct answer is:
does not exist
does not exist
$$
\begin{aligned}
& \lim _{x \rightarrow 2} \frac{\sqrt{2 \sin ^2(x-2)}}{x-2} \\
& \lim _{x \rightarrow 2} \frac{\sqrt{2}|\sin (x-2)|}{x-2} \\
& \text { R.H.L. }=\sqrt{2}, \text { L.H.L. }=-\sqrt{2}
\end{aligned}
$$
Limit does not exist.
\begin{aligned}
& \lim _{x \rightarrow 2} \frac{\sqrt{2 \sin ^2(x-2)}}{x-2} \\
& \lim _{x \rightarrow 2} \frac{\sqrt{2}|\sin (x-2)|}{x-2} \\
& \text { R.H.L. }=\sqrt{2}, \text { L.H.L. }=-\sqrt{2}
\end{aligned}
$$
Limit does not exist.
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