# Thread: Proving a function is continuous

1. ## 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

2. Originally Posted by xyz

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: $|\sin x|\leq1$