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Q.
Suppose $f (x)$ is differentiable at x = 1 and $\lim_{h \to 0} $ $\frac{1}{h} $f(1+h) = 5, then f '(1) equals
Application of Derivatives
Solution:
$f' \left(1\right) =\lim_{h \to0} \frac{f\left(1+h\right) -f\left(1\right)}{h};$
As function is differentiable so it is continuous as it is given that
$ \lim_{h \to0} \frac{f\left(1+h\right)}{h} $
= 5 and hence f (1) = 0
Hence $f'\left(1\right) = \lim_{h \to0} \frac{f\left(1+h\right)}{h} = 5 $