Functions Question 197
Question: If $ \underset{x\to 5}{\mathop{\lim }},\frac{x^{k}-5^{k}}{x-5}=500 $ , then the positve integral value of k is
[MP PET 1998]
Options:
A) 3
B) 4
C) 5
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
We know that, $ \underset{x\to a}{\mathop{\lim }}\frac{x^{n}-a^{n}}{x-a}=n{a^{n-1}} $ \ $ \underset{x\to 5}{\mathop{\lim }},\frac{x^{k}-5^{k}}{x-5}=k{{(5)}^{k-1}} $ ; But given, $ \underset{x\to 5}{\mathop{\lim }}\frac{x^{k}-5^{k}}{x-5}=500 $ , \ $ k{{(5)}^{k-1}}=500 $ ; $ k,{{(5)}^{k-1}}=4,{{(5)}^{4-1}},\therefore ,k=4 $ .
BETA
