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

                                        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$$LHL\neq RHL$f(x) is not continuous at x = 2Similarly you can find Left Hand Derivetive & Right Hand Derivative$LHD=\lim_{x\rightarrow 2^{-}}\frac{f(x+2)-f(2)}{x}$$RHD=\lim_{x\rightarrow 2^{+}}\frac{f(x+2)-f(2)}{x}$f(x) is not differentiable at x = 2Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

4 months ago

More Questions On Differential Calculus

Post Question

Vouchers
To Win!!!
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

 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,...

 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...

 Saurabh Kumar 25 days ago
.∫(e 200x +e 202x)/ (e x +e -x )dx.

 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

 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

 Arun Kumar 3 months ago
View all Questions »