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Question

Mathematics Question on limits and derivatives

lim⁡x→0sin⁡∣x∣x\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x} is equal to

A

1

B

0

C

positive infinity

D

does not exist

Answer

does not exist

Explanation

Solution

lim⁡x→0sin⁡∣x∣x\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}
LHL=−1,RHL=1LHL =-1, RHL =1
Limit does not exist.