Total Price:

There are no items in this cart.
Continue Shopping

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

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

3 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
9 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
See attachment sir please explain this question …...I’ll be very great full
Ans: Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty
Jitender Singh 8 months ago
milind 8 months ago
milind 8 months ago
please solve this question
Ans: Hello Student, Please find answer to your question below Your question is not clear. Please reupload the image. The first part of numerator: Is it e raise to power fraction part of...
Jitender Singh 6 months ago
no sir it is e raise to power integer part of x part of x
milind 6 months ago
​Q . TOTAL NUMBER OF SOLUTIONS OF - 2 X + 3 X + 4 X – 5 X = 0 IS=?
divide the whole equation with 5^x and you will get ans 1
Abhishek Singh 2 months ago
according to me it is no solution
srikar 4 months ago
its 1
archi gupta 4 months ago
No. of solution to the equation. [y+[y]]=2cos x where y=[sinx+[sinx+[sinx]]]/3 where [] denotes greatest integer function.
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
Arun Kumar 8 months ago
prove pythagoras theorem using trigonometry..........................plz explain briefly
Pythagorean Theorem, The theorem states that: "The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs”. This theorem is talking about...
Saurabh Kumar 4 months ago
For a right angled triangle, with sides P(perpendicular), B(base) and H(hypotenuse); write the trig. ratios in terms of P, B and H with any of the internal angle of the triangle. Using the...
Ravi 4 months ago
Hi Student We know using trigonometry sin = p/h and cos = b/h and using identity sin 2 + cos 2 =1 p 2 /h 2 +b 2 /h 2 =1 p 2 + b 2 = h 2 (Hence proved)
Harsh Patodia 4 months ago
tan^6 180/9 – 33 tan^4 180/9 + 27 tan2 180/9 is
Hello student, Please find the answer to your question below tan^6 180/9 – 33 tan^4 180/9 + 27 tan2 180/9 = take tan square common tan 2 20( tan 4 20 – 33 tan 2 20 + 27 ) now you...
Nishant Vora 6 months ago
View all Questions »