Struggling with analysis math

1. May 19, 2005

curlyc3

Hi! I'm struggling with analysis at the moment and here's one question that I'm struggling with! COuld somebody please explain what I need to do, using a delta/epsilon definition
The question is:

Define what it means for a function f to be continuous at a point a.

(a) Prove directly from your definition that f(x) = x^3 is continuous
everywhere.

(b) Give an example of a function that is continuous except at
x = 1, where it is not continuous.

Thanks

2. May 19, 2005

heman

u can see the reply of Matt Grime in the post epsilon and delta....

3. May 19, 2005

mathman

f(x)=0 ,x<1
f(x)=1 ,x>1

4. May 19, 2005

arildno

$$f(x)=2.3456712345, x\neq{1}, f(1)=-\frac{\pi^{tan(Sinh(0.5))}}{3.77}$$

Last edited: May 19, 2005