# epsilon-delta proof

• Oct 26th 2009, 02:51 PM
twostep08
epsilon-delta proof
Use the (epsilon-delta) definition of continuity to prove that f (x) = x^2 is continuous at every point in the interval [-10,10].

I have an exam coming up tomorrow, and i have absolutely no idea how to do this. I have watched the teacher do it time and time again, but nothing seems to help. The above is an example of something we should "know" and i dont even know where to begin. If someone could explain this as elementarily as possible I would be ridiculously thankful
• Oct 26th 2009, 02:55 PM
Jameson
If you have no idea how to start, you need to review the basics of delta-epsilon proofs.

Look at this tutorial to start and see if you can start the problem. If not, we'll help.

http://www.mathhelpforum.com/math-he...ta-proofs.html
• Oct 26th 2009, 07:28 PM
twostep08
i kind of understand one-degree functions now. but the suare root is still throwing me off. not to mention, i dont know how to relate limits to the problem i was given.... from what i did from the link you gave, i got abs(x-10)<E/M, but im still completely lost

also, i dont understand
1. Let
f (x) be defined by

f
(x) =

sin 1/x if x doesnt equal 0 and 1/2 when x=0

justify if f is continuous using the epsilon-delta definition of continuity