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


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

2 years ago

Share

Answers : (1)

                                        
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
4 months ago

Post Your Answer

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
f(x) = maximum {4, 1+x^2, x^2 -1}, x belong R. total no of points where fx is non differentiable ? graphical approach if possible
 
 
Hi Arpit, First note that x^2 + 1 > x^2 – 1 for all x belonging to R Therefore, max{4, x^2 -1, x^2+1} = max{4, x^2 + 1} Now, x^2 + 1 is a quadratic expression and opens upwards. To find the...
 
Asish Mahapatra one month ago
 
thank u for your help
 
Arpit Dhankar one month ago
If co domain is not given and we have to tell it is into or onto . How will we tell?
 
 
Ans: If co domain is not specified, we take it as a set of real numbers . Now you can check, whether range is set of real numbers or a subset of real number. If it is a set of real number,...
  img
Jitender Singh 3 months ago
it has been quite a while since my doubts havent been taken up. its my sincere request to clear them asap.
 
 
Yeah sure, we would like to draw one last request to you, actually, it was very tedius to find your previous questions, so will you paste your all the questions in one page, that oit would...
  img
Saurabh Kumar 25 days ago
.∫(e 200x +e 202x)/ (e x +e -x )dx.
 
 
Ans: Hello Sudent, Please find answer to your question below
  img
Jitender Singh 2 months ago
f:X to Y f(x)=sinx+cox+2root2 is invertible then X to Y is
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
A straight line makes an intercept on the y-axis twice as long as that on the x-axis and is at a unit distance from the origin. Determine its equation.
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
View all Questions »