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


Answers : (1)

f(x) = \left \{ 3-x^{2}, -1\leq x< 2 \right \}
f(x) = \left \{ 2x-4, 2\leq x\leq 4 \right \}
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
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
3 months ago

Post Your Answer

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
How is sin^-1 x = cos^-1 Y is equals to. y = (1-x^2 )^ 1/2. Please explain sir
Ans: Let Thanks & Regards Jitender Singh IIT Delhi askIITian Faculty
Jitender Singh 2 months ago
Image attached ….....
Hello student, Please find answer to your question Similarly, you can prove for n,
Jitender Singh 2 months ago
Sir explain this solution. I n = d n-1 /dx n-1 [x n-1 + nx n-1 log x ] In = (n-1) d n-2 / dx n-2 x n-2 + n d n-1 / dx n-1 (x n-1 logx) I n = (n-1 ) ! + nI n-1 In – nI n-1 =(n-1)! Proved
milind 2 months ago
Let A = lim(x -> -2) [tan(pi.x)/x+2] + lim (x → inf) (1 + 1/x 2 ) x Prove that A > 4
Ans:Hello student, please find answer to your question It is zero by zero form, apply L’Hospital Rule Hence, Proved
Jitender Singh 2 months ago
Find the real values of the parameter ‘a’ for which atleast one complex number z =x+iy satisfies both the equality | z- ai | = a+4 and the inequality | z-2 |
Hello Student, Please find the answer to your question below [|z-ai| = a + 4] [|z-2| < 1] For these two to have atleast one solution, then both circles must intersect [|x+iy-ai| = a+4]...
if 2 vectors a and b have their resultant as c also their sum is c. find the angle between a and b ?
angle=cos^-1[(a.b)/(mod a.mod b)]
Miryala Gopalakrishna 29 days ago
Two circles are constructed taking two sides of a triangle as a diameter then the probability of these two circle intesecting on the 3rd side is
Hello Student, Let circles are drawn on AB and AC of ABC Let there point of intersection other than A be D as AB is diameter of circle at AB we get ABD=pi/2 as AC is diameter of circle at AC...
Arun Kumar 2 months ago
View all Questions »