Question

Is f defined by $f\left(x\right)=\{\begin{array}{ccc}\frac{\sin 2x}{x}& if& x\ne 0\\ 1& if& x=0\end{array}$ continuous at $0$.

• A. True
• B. False

Answer 1

The correct option is B False

$RHL=LHL=\underset{x\to 0}{lim}\frac{2\sin 2x}{2x}=2$

Value of $f\left(x\right)$ at $x=0$, we have $f\left(x\right)=1$

hence, it is not continuous at x=1.