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please explain fully ….if it has 0/0 form …..then please tell why

please explain fully ….if it has 0/0 form …..then please tell why

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Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below
Since f’’(x) is continuous at x = 0, then f(x) & f’(x) should exist & continuous at x = 0.
The limit of the function should exist at x = 0.
For the limit to exist,
f(x) = x^n + c, n\geq 2, c = constant
f'(x) = n.ax^{n-1}
f''(x) = n.(n-1).ax^{n-2}
Since
f''(0) = 4
\Rightarrow n-2 = 0
\Rightarrow n=2
2.(2-1)a = 4
a = 2
f(x) = 2x^{2} + c
Now you can see that we have 0/0 form both in case of f(x) & f’(x).

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