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The value of \( \lim _{x \rightarrow 0} \frac{f(2+h)-f(2-h)}{h} \)is equal to |
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Answer» \(\lim\limits_{x\to 0} \frac{f(2 + h)- f(2 -h)}{h}\) \(= \lim\limits_{x\to 0} \frac{f(2 +h)- f(2 + f(2) - f(2 -h))}{h}\) \(= \lim\limits_{x\to 0} \frac{f(2 +h) - f(2)}{h} + \lim\limits_{h\to 0} \frac{f(2 -h) - f(2)}{-h}\) \(= f'(2) + f'(2)\) \(= 2f'(2)\). |
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