A) 6
B) 3
C) 12
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{2f(x)-3f(2x)+f(4x)}{{{x}^{2}}}\left[ \frac{0}{0}\text{form} \right]\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2f'(x)-6f'(2x)+4f'(4x)}{2x}\] [using L-Hospital's rule] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2f''(x)-12f''(2x)+16f''(4x)}{2}\] [using L?Hospital?s rule] \[=\frac{2f''(0)-12f''(0)+16f''(0)}{2}\] \[=3f''(0)=3\times 2=6\] 3You need to login to perform this action.
You will be redirected in
3 sec