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

2 months ago

More Questions On Differential Calculus

Post Question

Vouchers
To Win!!!
i am posting this question from 5 days …..is there anybody who can help me ….….….…...

Ans: Let the resultant of vectors A & B to be C Angle b/w A & C Angle b/w B & C Or you can always say that the resultant will fall toward the vector which have more magnitude.

 Jitender Singh one month ago
Find the number of point of discontinuity of the function in 0 to 2(pi). f(x) = [sinx + cosx] [] is an integral part function.

 Jitender Singh one month ago
The smallest postive integer for which (1+i/1-i)^n=1

Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty

 Arun Kumar one month ago
if secA+tanA=x,then what are the values of sinA,secA,tanA

secA+tanA=x.........(1.) and we know that sec 2 A-tan 2 A=1 ON DIVIDING with given result with eqn.1secX-tanX=1/x(2.) now solve eqn(1.)and(2.) by simple linear equation method to obtain...

 siddharth gupta one month ago
Find the equation of the lines which pass through the point of intersection of the lines 4x-3y-1=0 and 2x-5y+3=0 and are equally inclined to the axes.

Intersection point of 4x-3y-1=0 & 2x-5y+3=0 is (1,1). if lines are equally inclined with the axes then slope of lines either 1 or -1. so equations of lines are y-1=1(x-1) & y-1=-1(x-1)...

 sunil raikwar 2 months ago
View all Questions »