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 ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Relation between Continuity and Differentiability

Given that f ...

Question

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Suggest Corrections

Similar questions

f (x) = {\begin{matrix} 4 x - 3, & x < 1 x^{2} & x \geq 1 \end{matrix},

lim x \to 1 f (x) =

If ${\begin{matrix} \frac{x^{2} - x}{2 x}, x \neq 0 k, x = 0 \end{matrix}$ and if f is continuous at x=0,then k=?

f (x) = {\begin{matrix} e^{\frac{1}{x}}, & w h e n & x \neq 0 0, & w h e n & x = 0 \end{matrix}

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{sin [x]}{[x]}, & [x] \neq 0 0, & [x] = 0 \end{matrix},

lim x \to 0 f (x)

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x - 1, & x < 0 \frac{1}{4}, & x = 0 x^{2}, & x > 0 \end{matrix}

Join BYJU'S Learning Program