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Differential Calculus> please explain fully ….if it has 0/0 form...

question mark

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

milind , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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