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Given that \mathrm{ f(x)= \begin{cases}\frac{x g(x)}{|x|}, & x \neq 0 \\ 0, & x=0\end{cases} } \mathrm{g(0)=g^{\prime}(0)=0 \, \, then \, \, f^{\prime}(0)} is equal to

Option: 1

1


Option: 2

-1


Option: 3

2


Option: 4

None of these 


Answers (1)

best_answer

\mathrm{f(x) \text { is continuous at } x=0}

\mathrm{f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}=\lim _{h \rightarrow 0} \frac{\frac{h g(h)}{h \mid}-0}{h}=\lim _{h \rightarrow 0} \frac{g(h)}{|h|}=0}

\mathrm{=\lim _{h \rightarrow 0} \frac{g^{\prime}(h)}{1}=0 \text {. }}

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Devendra Khairwa

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