# Proving a function is continuous

• November 18th 2009, 07:59 PM
xyz
Proving a function is continuous
it is continuous because f(0) = 0. However, I'm not clear how to find such delta. We have to find a positive delta such that |f(x) - f(0)| < epsilon = |x sin(x) | < epsilon when |x sin x| < delta.

How to find such delta? Does delta = epsilon? I'm not clear
• November 18th 2009, 08:01 PM
RockHard
• November 18th 2009, 08:25 PM
redsoxfan325
Quote:

Originally Posted by xyz
http://i291.photobucket.com/albums/l...Capture887.jpg

Ofcourse it is continuous because f(0) = 0. However, I'm not clear how to find such delta. We have to find a positive delta such that |f(x) - f(0)| < epsilon = |x sin(x) | < epsilon when |x sin x| < delta.

How to find such delta? Does delta = epsilon? I'm not clear

Prove: $|x|<\delta \implies |x\sin x|<\epsilon$.

Hint: $|\sin x|\leq1$