Wednesday, 18 August 2021
Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be any twice differentiable function such that its second derivative is continuous and
\[\frac{d f(x)}{d x} \neq 0 \text { for all } x \neq 0 \text { . }\]
If then prove that
\[\lim _{x \rightarrow 0} \frac{f(x)}{x^{2}}=\pi\]
for all \(x \neq 0, \quad f(x)>f(0).\)
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