Question

If function $f\left(x\right)=\frac{x^3-a^3}{x-a}$, is continuous at $x=a$ then the value of $f\left(a\right)$ is-

• A. $2a$
• B. $2a^2$
• C. $3a$
• D. $3a^2$

Answer 1

The correct option is D $3a^2$

$f\left(x\right)=\frac{x^3-a^3}{x-a}$
Since, $f\left(x\right)$ is continuous at $x=a$
$\therefore$ ${lim}_{x\to a}f\left(x\right)={lim}_{x\to a}\frac{x^3-a^3}{x-a}$
$=3{\left(a\right)}^{3-1}$ (${lim}_{x\to a}\frac{x^n-a^n}{x-a}=n{a}^{n-1}$)
$=3a^2$