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Question
If f (x) is differentiable at x = c, then write the value of
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Solution
Given:
\[\lim_{x \to c} f(x) = \lim_{x \to c} \left[ \left\{ \frac{f(x) - f(c)}{x - c} \right\} (x - c) + f(c) \right]\]
\[ \lim_{x \to c} f(x) = \lim_{x \to c} \left[ \left\{ \frac{f(x) - f(c)}{x - c} \right\} (x - c) \right] + f(c)\]
\[ \lim_{x \to c} f(x) = \lim_{x \to c} \left\{ \frac{f(x) - f(c)}{x - c} \right\} \lim_{x \to c} (x - c) + f(c)\]
\[ \lim_{x \to c} f(x) = f'(c) \times 0 + f(c) = f(c)\]
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