Home
Class 12
MATHS
Let f(x)={{:((1)/(x^(2))sin(x^(2))," whe...

Let `f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):}`
Discuss the continuity of f (x) at x = 0 .

Text Solution

Verified by Experts

The correct Answer is:
Therefore , the function f (x) is differentiable at x = 0 .
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A (Multiple Choice Type questions)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A (Very short Answer Type Questions)|16 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

Similar Questions

Explore conceptually related problems

Given , f(x)={{:((sin5x)/(3x),"when "xne0),((3)/(5),"when "x=0):} Examine the cotinuity of f (x) at x = 0 .

If f(x)={{:((|sinx|)/(x),"when "xne0),(1,"when "x=0):} then examine the continuity of the function at x = 0.

Let , f(x)=1/xsin(x^2) when x ne0 =0 when x=0 Discuss the continuity and differentiability of f(x) at x=0.

A function phi(x) is defined as follows: phi(x)={{:((tan4x)/(5x)," when " xne0),((5)/(4)," when "x=0):} Examine the cotinuity of phi(x) at x=0 .

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " x =0):} If f (x) is continuous at x = 0 , find the value of alpha .

Let f(x)={{:(" "x^(2)/(2),"when " 0lexlt1),(2x^(2)-3x+(3)/(2),"when " 1 lexle2):} Discuss the continuity of (x) in the interval 0lexle2 .

Draw the graph of the function " "y=f(x)={:{(|x|/x",","when "x ne 0),(0",","when "x = 0):} From the graph examine the continuity of f(x) at x = 0.

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

Let f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2)),"when " xne2),(" "k,"when " x=2):} if f (x) is continuous for all x , find k.