(D) To find the limit $\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$, we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.For $x <

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(D) To find the limit $\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$, we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.For $x For $x > 0$, $|x| = x$, so $\lim _{x \rightarrow 0^+} \frac{\sin x}{x} = 1$.Since the left-hand limit $(-1)$ is not equal to the right-hand limit $(1)$, the limit does not exist.

Class 11 Mathematics Limits Concept of limits, Evaluation of algebric limits

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$\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

WBJEE 2010 All WBJEE

A
$1$
B
$0$
C
positive infinity
D
does not exist

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Limits

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Concept of limits, Evaluation of algebric limits

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$\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

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