Question

Evaluate $\underset{x\to 0}{lim}\frac{\sin x}{|x|}$.

• A. $1$
• B. $0$
• C. $-1$
• D. does not exist

Answer 1

The correct option is D does not exist

Left hand limit is $=-\underset{x\to 0^{-}}{lim}\frac{sinx}{x}=-1$

And right hand limit is $=\underset{x\to 0^{-}}{lim}\frac{sinx}{x}=1$

Clearly both are not equal, hence limit does not exist.