0

Guest

Courses New

if f(x) = { 3-x2 , -1[_x[_2 { 2x-4 , 2[_x[_4 then find fof(x)and discuss the continuty and differentiability

if f(x) = { 3-x2 , -1[_x[_2


            { 2x-4 ,  2[_x[_4 then find fof(x)and discuss the continuty and differentiability

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
f(x) = \left \{ 3-x^{2}, -1\leq x< 2 \right \}
f(x) = \left \{ 2x-4, 2\leq x\leq 4 \right \}
Continuity,
Left Hand Limit(LHL) = Right Hand Limit(RHL) = f(2)
LHL = \lim_{x\rightarrow 2^{-}}3-x^{2} = -1
RHL = \lim_{x\rightarrow 2^{+}}2x-4 = 1
LHL\neq RHL
f(x) is not continuous at x = 2
Similarly you can find Left Hand Derivetive & Right Hand Derivative
LHD=\lim_{x\rightarrow 2^{-}}\frac{f(x+2)-f(2)}{x}
RHD=\lim_{x\rightarrow 2^{+}}\frac{f(x+2)-f(2)}{x}
f(x) is not differentiable at x = 2
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More