Question

If $\underset{x\to 5}{lim}\frac{x^k-5^k}{x-5}=500$, then the positive integral value of $k$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

$\underset{x\to 5}{Lim}$ $\frac{x^k-5^k}{x-5}$

$=\frac{0}{0}$ form

Applying $L^{\prime }$ Hospital Rule

$k{x}^{k-1}=500$

When $k=4$, the equation is satisfies.

$k=4$ Answer (B).