Question-26
\text { If } \lim _{x \rightarrow 5} \frac{x^{k}-5^{k}}{x-5}=500 \text {, then } k \text { is equal to }A) 3
B) 4
C) 5
D) 6
Answer: B) 4
Explanation
Let \lim _{x \rightarrow 5} \frac{x^{k}-5^{k}}{x-5}=500
By using \lim _{x \rightarrow a} \frac{x^{n}-a^{n}}{x-a}=n \cdot a^{n-1}, we have
\Rightarrow k \cdot 5^{k-1}=500 \Rightarrow k \cdot 5^{k-1}=2^{2} 5^{3}Comparing both the sides, k-1=3 \Rightarrow k=4.