Functions Question 308
Question: Let $ f:R\to R $ be a differentiable function having $ f(2)=6,f’(2)=( \frac{1}{48} ). $ Then $ \underset{x\to 2}{\mathop{\lim }},\int\limits_6^{f(x)}{\frac{4t^{3}}{x-2}} $ dt equals
[AIEEE 2005]
Options:
A) 12
B) 18
C) 24
D) 36
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 2}{\mathop{\lim }},\frac{\int\limits_6^{f(x)}{4t^{3}dt}}{x-2}(0/0,form)=\underset{x\to 2}{\mathop{\lim }},\frac{4{{(f(x))}^{3}}\times f’(x)}{1} $ $ =4{{(f(2))}^{3}}\times f’(2)=18 $ .
BETA
