Question

$\underset{x\to 2}{\lim }\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right)$

• A. equals $\frac{1}{\sqrt{2}}$
• B. Does not exist
• C. equals $\frac{1}{\sqrt{2}}$
• D. equals $-\sqrt{2}$

Answer 1

Answer: (B)

$\underset{x\to 2}{\lim }\left(\frac{\sqrt{1-\cos 2(x-2)}}{x-2}\right)$
$=\underset{x\to 2}{\lim }\frac{\sqrt{2}|\sin (x-2)|}{x-2}$
which doesn't exist as $LHL=-\sqrt{2}$ whereas
$RHL=\sqrt{2}$