iran-konkur 2017 Q118

iran-konkur · Other · konkur-riazi_1396_specialized Differentiation from First Principles
118. If $f$ is differentiable at $x = 4$ and $\displaystyle\lim_{x \to 4} \frac{f(x) + 5}{x - 4} = \frac{-3}{2}$, then $\dfrac{f(2x)}{x}$ at $x = 2$ equals:
(1) $-\dfrac{1}{4}$ (2) $-\dfrac{1}{2}$ (3) $\dfrac{1}{4}$ (4) $\dfrac{1}{2}$
\textbf{118.} If $f$ is differentiable at $x = 4$ and $\displaystyle\lim_{x \to 4} \frac{f(x) + 5}{x - 4} = \frac{-3}{2}$, then $\dfrac{f(2x)}{x}$ at $x = 2$ equals:

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(1) $-\dfrac{1}{4}$ \hfill (2) $-\dfrac{1}{2}$ \hfill (3) $\dfrac{1}{4}$ \hfill (4) $\dfrac{1}{2}$

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