Question

Find the value of $a$ so that the function $f\left(x\right)=\{\begin{array}{c}\sin 2ax,x\ne 0\\ x^2,x=0\end{array}$ is continuous at $x=0$

Answer 1

$f\left(x\right)=\{\begin{array}{cc}\sin 2ax& ,x\ne 0\\ x^2& ,x=0\end{array}$

$\underset{x\to 0}{lim}=f\left(0\right)$

$\Rightarrow \underset{x\to 0}{lim}\sin 2ax=x^2$

$\therefore 0=x^2$

$\therefore x=0$

$f\left(x\right)$ is continious at $x=0\forall aϵR$