# Talk:Limit

## Contents

#### Abram 7/10

I second Anna's comments. One additional thing:

//The limit at x=0 of $f(x) = x^2\,$ would pretty clearly be 0, since $f(0)=0$. //

The word "since" implies logical caustion, that is, the statement basically says: "Because f(0) = 0, the limit at x=0 of $f(x) = x^2\$ is 0." However, the whole point of your next statement (which is correct) is that this is not a valid chain of logic: the fact that f(0) = 0 does not tell you anything about the limit. Can you reword this sentence?

Also, you should use limit notation here instead of saying "the limit at x = 0".

#### Anna 7/9

I just saw "What this means to us is that for every region of positive radius \varepsilon at a given point, there is a "

umm... a what? Also, you need some math tags. But this should be easy to fix.... I know that sentence is going somewhere!

#### Anna 7/6

In your formal definition, I'd really like to see an explanation of how that definition relates to the intuitive definition. You can explain how it relates to shrinking something down smaller and smaller... something along those lines. For someone who's quite good at explaining this in basic terms, you might want to talk to Deb Bergstrand.

#### Alan 6/25

Your beginning informal definition, maybe something like "As the variable x gets close to the number a, it may happen that the function f(x) gets close to the number L. We then say the limit of f(x) as x approaches a is L" or something. Then give notation.

Before Intuitive Def maybe put "We'll see what 'arbitrarily' means precisely in the rigorous definition below" or something.

Intuitive Def--this ain't really a definition, is it?

I would argue that it is an informal basic definition. Most high school calculus students probably define a limit in this intuitive way, as opposed to the more rigorous definition presented later.

"But this is a special case, in the majority of limits" cases? "cannot be solved in this manner"--you didn't solve it in that manner either.

I'm not sure I follow.

For your rigorous def (of limit not A limit?)it would be way cool to have an interactive diagram in which changing the size of epsilon shows a corresponding delta, or something. You've got a lot on your plate so maybe just challenge future generations to do this.

Put on ideas for future.

#### Gene 6/25

Hey Alan, good for you for tackling this needed helper page! You're off to a good start, too. I've made lots of comments because I think this is important.

Your beginning informal definition, maybe something like "As the variable x gets close to the number a, it may happen that the function f(x) gets close to the number L. We then say the limit of f(x) as x approaches a is L" or something. Then give notation.

Before Intuitive Def maybe put "We'll see what 'arbitrarily' means precisely in the rigorous definition below" or something.

Intuitive Def--this ain't really a definition, is it?

"The limit at x=0, would simply be f(x)=0, since as the function is continuous and differentiable at every point, f(0) = 0." How about "The limit at x=0 of f(x) = x^2 would pretty clearly be 0" and forget about "the function is continuous and differentiable at every point" which doesn't really play in the intuitive understanding.

"But this is a special case, in the majority of limits" cases? "cannot be solved in this manner"--you didn't solve it in that manner either.

Begin the next "For a very different example" and make the f(0)=1 much more vivid in the graph.

"f(x) is not continuous at x = 0 (as shown on the right)." Do you want to mention this now? (and what's this as shown on the right??)

Next eg: "as approaching the limit from different sides". Do you want "because" rather than "as"? How about saying what the function is beside the graph?

For your rigorous def (of limit not A limit?)it would be way cool to have an interactive diagram in which changing the size of epsilon shows a corresponding delta, or something. You've got a lot on your plate so maybe just challenge future generations to do this.

Properties of limits, not A limit? You need to have x->a, etc throughout.