If $\lim _{\mathrm{x} \rightarrow 5} \frac{\mathrm{x}^{\mathrm{k}}-5^{\mathrm{k}}}{\mathrm{x}-5}=500$, then the value of $\mathrm{k}$, where $\mathrm{k} \in \mathrm{N}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow 5} \frac{x^k-5^k}{x-5}=500 \ & 	herefore(k)(5)^{k-1}=500 \ & =4(125)=4(5)^3=4(5)^{4-1} \ & 	herefore k=4\end{aligned}$

If $\lim _{\mathrm{x} \rightarrow 5} \frac{\mathrm{x}^{\mathrm{k}}-5^{\mathrm{k}}}{\mathrm{x}-5}=500$, then…

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