MY CART (5)
ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
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

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
8 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
TANGENTS & NORMALS show that the curves 2x=y^2 and 2xy=k cut at right angles if k^2=8
 
 
Ans: Hello student, Please find the answer to your question below Slope of tangent: …..............(1) Slope of tangent: ...............(2) Put in the equation of curves:
  img
Jitender Singh 5 months ago
Prove that
 
 
let y = f(x) g(x) Taking log on both sides log y= g(x) log(f(x)) Taking antilog on both sides y = e g(x) logf(x) Consider log f(x)= log ( 1 + (f(x)-1)) Expansion of log ( 1 + x)= x – x...
  img
Harsh Patodia 4 months ago
 
Hi Student, Basically subtraction of 1 comes from the derivation. So it must be done. If you want to know the derivation please reply on this thread otherwise its not necessary. You can...
  img
Harsh Patodia 4 months ago
 
Hi student This is of the type f(x) g(x) which is of form 1 such that f(x) 1 and g(x) Solution of such form is give by e g(x)(f(x)-1) When you will subsitute appropriate values of f(x) and...
  img
Harsh Patodia 4 months ago
Let f : A-> A where A = { 1, 2, 3, 4, 5} such that ff(x) = x . How many such functions are possible
 
 
First note that the function is injective: f(x) = f(y) implies f(f(x)) = f(f(y)) which yields x = y. We say that a number x is fixed by f if f(x) = x. Now, if f(a) = b, with a and b unequal,...
 
mycroft holmes 5 months ago
 
In general the real functions which satisfies the condition that fof(x) = x are (i) f(x) = a – x where a is any real no. (ii) f(x) = x But here, f: A → A is the function which should satisfy...
 
Y RAJYALAKSHMI 5 months ago
 
Pl. ignore this solution – it is incomplete
 
Y RAJYALAKSHMI 5 months ago
log base 24 54 = a and log base 12 18 = b Then the value of [ab-5(a-b)].
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 7 months ago
Q . PLEASE INTEGRATE THE FUNCTION WHOSE PIC IS ATTACHED.....
 
 
divide num and denom. by x^2, then substitute ax + b/x = t.
 
Nihal Raj 4 months ago
 
divide num and denom. by x^2, then substitute ax + b/x = t.
 
Nihal Raj 4 months ago
 
thanks
 
bharat makkar 4 months ago
please solve this question without substituion method which of the following is true (a,b,c>0)? 2(a^3 b^3 +c^3) greater than or equal bc(b+c) +ca(c+a) + ab(a+b) (a^3 + b^3 + c^3)/3 greater...
 
 
Hello student, Please find the answer to your question below (a)First you need to prove that for positive values of x and y x/y + y/x >= 2 (x - y)² + 2xy = x² + y² Divide...
  img
SHAIK AASIF AHAMED 7 months ago
 
We now Arithmatic mean (AM) > Harmonic mean (HM) ie., between any two number a,b (a+b)/2 >2ab/(a+b) => 2/(a+b) => 2/(a+b) similarily 2/(b+c) So, 2/(b+c) + 2/(c+a) + 2/(a+b) =>2/(b+c)...
 
Y RAJYALAKSHMI 7 months ago
View all Questions »