Differentiation Question 392
Question: If $ f(x) $ is a differentiable function and $ {f}’’(0)=a $ then $ \underset{x\to 0}{\mathop{\lim }}\frac{2f(x)-3f(2x)+f(4x)}{x^{2}} $ is
[Orissa JEE 2004]
Options:
A) 3a
B) 2a
C) 5a
D) 4a
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{2f(x)-3f(2x)+f(4x)}{x^{2}} $
Using L-Hospital’s rule twice, we get $ \underset{x\to 0}{\mathop{\lim }}\frac{2f’’(x)-3.2.2f’’(2x)+4.4f’’(4x)}{2}=3a $ { $ \because $ Given $ f’’(0)=a $ }.
BETA
