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help expain fully

help expain fully

Question Image
Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans: ©
L = \lim_{x\rightarrow 0}\frac{2f(x)-3f(2x)+f(4x)}{x^{2}}
Limit of f’’(x) at x = 0 exists.
f''(0) = 4
Other data should be given which make the limit zero by zero form
f'(0) = 0
f(0) = 0
So it is zero by zero form. Apply L’hospital rule
L = \lim_{x\rightarrow 0}\frac{2f'(x)-3.2f'(2x)+4f'(4x)}{2x}
L = \lim_{x\rightarrow 0}\frac{2f''(x)-3.2.2f''(2x)+4.4f''(4x)}{2}
L = \frac{2f''(0)-3.2.2f''(0)+4.4f''(0)}{2}
L = \frac{6f''(0)}{2}
L = 3f''(0) = 3.4 = 12

milind
23 Points
7 years ago
jitendra sir can you tell me how it is 0/0 form ….….…...no ther data is given....please

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