Given that f x - left matrix fracx - gx-x- - x neq 0 10- - x -0lend matrix right- g0-0-g-0- then f-0 equalsA- 1B- -1C- 2D- 0

The correct option is D 0f'(0)=limh→0f(0+h) f(0)/h =limh→0hg(h)/|h| 0/h=limh→0g'(h)/1=0 ...

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Relation between Continuity and Differentiability

Given that f ...

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Given that f(x) = $⎧ ⎨ ⎩ \begin{matrix} \frac{x . g (x)}{| x |}, & x \neq 0 0, & x = 0 \end{matrix}$ g(0) = 0 = g'(0), then f'(0) equals

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