If       

  • Option 1)

    continuous for all x, but not differentiable at x=0

  • Option 2)

    neither differentiable not continuous at x=0

  • Option 3)

    discontinuous everywhere

  • Option 4)

    continuous as well as differentiable for all x

 

Answers (1)

As we learnt in 

Condition for differentiable -

A function  f(x) is said to be differentiable at  x=x_{\circ }  if   Rf'(x_{\circ })\:\:and\:\:Lf'(x_{\circ })   both exist and are equal otherwise non differentiable

-


 f(x)= \left\{\begin{matrix} xe^{-\left ( \frac{1}{\left | x \right |}+\frac{1}{x} \right )} \: \: \: \: \: x\neq 0\\ 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x=0 \end{matrix}\right.

Since, \left | x \right |\is\ not\ differential\ at\ x=0

            \left | x \right | \: is \: continuous \: at \: x=0

\therefore \: option \: 1 \: is \: correct


Option 1)

continuous for all x, but not differentiable at x=0

This option is correct

Option 2)

neither differentiable not continuous at x=0

This option is incorrect

Option 3)

discontinuous everywhere

This option is incorrect

Option 4)

continuous as well as differentiable for all x

This option is incorrect

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 6999/- ₹ 5/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions