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TIFR-2012-Maths-C: 28

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True/False Question:

Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that

$$\underset{h\rightarrow 0}{lim }\:\frac{f\left ( x+h \right )-f\left ( x-h \right )}{h}$$

exists for all $x \in \mathbb{R}$. Then $f$ is differentiable in $\mathbb{R}.$

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