Thread: For those that never learnt well the epsilon-delta proofs

I attach a paper based in how to prove limits by definition, pretty nice.

Hope it helps.

Thanks both my teacher at the high school and university level for some reason never thought this was important and just went directly to limits and derivatives without teaching the proofs.

LOL THANK YOU! my teacher was unclear about this...

Never has it been more clear...thank you so much. Now the definition of a limit in 3-D makes so much more sense. You are a saint for posting this! SO useful!

jajaj Krizalid thank you very much, as always, excellent input.

here's something for practice: using method, directly prove that:

calculus 1: if is a polynomial, then

calculus 2: if is a polynomial, then

Originally Posted by 11rdc11

Thanks both my teacher at the high school and university level for some reason never thought this was important and just went directly to limits and derivatives without teaching the proofs.

Student's eye glaze over when I mention this.
Plus books are dropping it, so don't blame your professors.
All books are becoming more and more watered down.
Some schools don't even teach trig substitution and I see hyperbolics are disappearing too...
Zill's DE book used to have lots of problems with cosh and sinh and now it hardly has any.
That stuff is really handy in DE.

If anyone is interested I have a few rigorous limit examples with animations on my web site for both epsilon-delta proofs and the epsilon-M proofs if you will for limits at infinity

Calculus 1

They are rougly in the middle of the page as I start with an intuitive approach leading up the roigorous definitions

I only began to understand Delta-Epsilon proofs well-past my BC calc days when I was taking an introductory proofs class. I think that most people going into or coming out of Calc just don't have proofs down enough yet to be able to whip one out.

thank you

Thanks for this

Nice! This paper is really good .

That is a very useful paper.It really makes stuff easier to understand.

Wow thanks very useful

thanks very much, it is very useful for me