Math Is Fun Forum

clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

Help with Delta-Epsilon proof for sinx.

If i let f(x) = sinx. Find the error E(x, pi/2) in equation:
E(x,a) = f'(a) - [(f(x)-f(a))/(x-a)]
as a function of x.  Graph E(x,a). Find a delta if epsilon = .01, .0001, 10^-10.

Honestly I can do the graphing part.  I will also be able to do the proof when epsilon = .0001, 10^-10 once I have seen a proof for one part.  I am having a hard time with the teacher - he has yet to do an example of how to do one of these proofs... and the book, needless to say, is not much better.

Any help would be great.

clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

Re: Help with Delta-Epsilon proof for sinx.

Actually... To show what I have done:

I found that

And that:

And then plug in that for the first part... but I'm not sure how that would help!????

Last edited by clooneyisagenius (2008-02-12 15:25:52)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Help with Delta-Epsilon proof for sinx.

So we want to show, using ε and δ, that

.

Given ε > 0, let

.

Note that

Similarly,

Hence, for all X such that 0 < |X| < δ,

Thus, given ε < π⁄2, you can simply set δ = ε.