iran-konkur 2018 Q111

iran-konkur · Other · konkur-riazi_1397_specialized Chain Rule Limit Involving Derivative Definition of Composed Functions
111- If $f(x) = \sqrt{x^2 - |x| + |x|}$, then $\displaystyle\lim_{h \to 0^+} \dfrac{f(1+h)-f(1)}{h}$ is which of the following?
(1) $\dfrac{1}{2}$ (2) $\dfrac{5}{4}$ (3) $\dfrac{3}{2}$ (4) $\dfrac{5}{2}$
\textbf{111-} If $f(x) = \sqrt{x^2 - |x| + |x|}$, then $\displaystyle\lim_{h \to 0^+} \dfrac{f(1+h)-f(1)}{h}$ is which of the following?

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(1) $\dfrac{1}{2}$ \hfill (2) $\dfrac{5}{4}$ \hfill (3) $\dfrac{3}{2}$ \hfill (4) $\dfrac{5}{2}$

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