MHB Prove/Disprove: Uniform Continuity of sin(sin(x))

[solakis1]

prove or disprove if the following function is uniformly continuous:

$$sin(sin(x)) $$ using the ε,δ definition

 

[HOI]

Do you know what that means? What IS the "$\epsilon, \delta$ definition"?

 

[topsquark]

Do you know what that means? What IS the "$\epsilon, \delta$ definition"?

This is a challenge problem. solaklis wants you to find the answer...

-Dan

 

[solakis1]

hint
[sp]Use the formula :
sinx-siny =$2cos\frac{x+y}{2}sin\frac{x-y}{2}$[/sp]

 

[solakis1]

Do you know what that means? What IS the "$\epsilon, \delta$ definition"?

The $\epsilon$ $\delta$ definition for real function f(x) is :

Given $\epsilon>0$ there exists a $\delta>0$ such that :
For all x,y belonging the to domain of f(x) and $|x-y|<\delta$ then $|f(x)-f(y)|<\epsilon$