Functions Question 10
Question: If $ f(9)=9 $ , $ f’(9)=4 $ , then $ \underset{x\to 9}{\mathop{\lim }} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}= $
[IIT 1988; Karnataka CET 1999]
Options:
A) 2
B) 4
C) -2
D) -4
Show Answer
Answer:
Correct Answer: B
Solution:
Applying L-Hospital’s rule, $ \underset{x\to 9}{\mathop{\lim }} \frac{\frac{1}{2\sqrt{f(x)}}\cdot {f}’(x)}{\frac{1}{2\sqrt{x}}}=\frac{\frac{{f}’(9)}{\sqrt{f(9)}}}{\frac{1}{\sqrt{9}}}=\frac{\frac{4}{3}}{\frac{1}{3}}=4 $
BETA
