Question

$\text{If}f\left(x\right)=\{\begin{array}{cc}\frac{sinx}{x},& x\ne 0\\ 1,& x=0\end{array},\text{then}{lim}_{x\to 0}f\left(x\right)=$is

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

Answer 1

The correct option is C

does not exist

$\underset{x\to 0}{lim}\frac{\left|sinx\right|}{x}\text{does not exist}\underset{x\to 0^{-}}{lim}\frac{-\left|sinx\right|}{x}=\underset{x\to 0^{-}}{lim}\frac{-\left|sinx\right|}{x}=-1\underset{x\to 0^{+}}{lim}\frac{\left|sinx\right|}{x}=\underset{x\to 0^{+}}{lim}\frac{\left|sinx\right|}{x}=1$