Home
Class 11
MATHS
If f is an odd function and if Lim(x to ...

If f is an odd function and if `Lim_(x to 0) f(x)` exists , prove that this limit must be zero .

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    ICSE|Exercise EXERCISE 18(A)|10 Videos

  • LIMITS

    ICSE|Exercise EXERCISE 18(B)|10 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS|17 Videos

  • LIMITS AND DERIVATIVES

    ICSE|Exercise Multiple Choice Questions |31 Videos

Similar Questions

Explore conceptually related problems

If f is an odd function and f(0) is defined, must f(0)=?

If f(x) = (x^(2)-9)/(x-3) , find it Lim_(x to 3) f(x) exists .

Let f be an even function and f'(x) exists, then f'(0) is

For the function f(x) = 2 . Find lim_(x to 1) f(x)

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

Prove that Lim_(x to 0) (|x|)/x , x != 0 does not exist .

If lim_(x->a)(f(x)/(g(x))) exists, then

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

If f is an even function , then prove that Lim_( xto 0^(-)) f(x) = Lim_(x to 0^(+)) f(x) , whenever they exist .