Question

Please answer this immediately

Answer 1

Answer:

Value of k is 4

Step-by-step explanation:

Formula used:

$\lim_{x \to{a}} \frac{x^n-a^n}{x-a}=n\:a^{n-1}$

Now

$\lim_{x \to5} \frac{x^k-5^k}{x-5}=500$

by using the above formula we get

$k\:a^{k-1}=500$

$k\:a^{k-1}=4*125$

$k\:a^{k-1}=4*5^3$

$k\:a^{k-1}=4*5^{4-1}$

comparing both sides we get

k =4