Question $7$

Let $f(x)=\{\begin{array}{cc}\frac{x^{2}x}{x},& x<mn>0</mn>\\ 1,& x=0\\ 2(x-1)& 3,& x>0\end{array}$

Which of the following statements are true of $f?$

I. $f$ is defined at $x=0.$

II$.\underset{x0}{lim}f(x)$ exists.

III. $f$ is continuous at $x=0.$

Only I and III are correct

Only III is correct

Only I and II are correct

I, II$,$ and III are correct

Only II and III are correct

Only II is correct

Only I is correct

Question $8$