Question

If $f\left(x\right)=\{\begin{array}{c}\frac{x^2}{a}-a,if0<x<a\\ \\ 0,ifx=0\\ \\ a-\frac{a^2}{x^2},ifx>a\end{array}$

then $\underset{x\to a}{lim}f\left(x\right)$ is equal to :

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

Answer 1

The correct option is A $0$

Solution -

$f\left(x\right)=\{\begin{array}{c}\frac{x^2}{a}-a,if0<x<a\\ 0,ifx=0\\ a-\frac{a^2}{x^2},ifx>a\end{array}$

${lim}_{x\to a}f\left(x\right)=LHL=RHL$

$LHL=\frac{a^2}{a}-a=0$

$RHL=a-\frac{a^2}{a}=0$

${lim}_{x\to a}f\left(x\right)=LHL=RHL=0$

A is correct