Question

$f\left(x\right)=\{\begin{array}{c}\frac{x^5-32}{x-2}\\ k,x=2\end{array},x\ne 2$ is continuous at $x=2$, then $k=.....$

• A. $16$
• B. $80$
• C. $32$
• D. $8$

Answer 1

The correct option is B $80$

Given $f\left(x\right)=\{\begin{array}{c}\frac{x^5-32}{x-2}\\ k,x=2\end{array},x\ne 2$
$\because$ $f\left(x\right)$ is continuous at $x=2$
$\therefore LHL=RHL=f\left(2\right)$
$f\left(2\right)=k$
Now, $\underset{x\to 2}{lim}\frac{x^5-32}{x-2}$
$=5.{\left(2\right)}^{5-1}$ ($\underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n{a}^{n-1}$)
$k=80$