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# Can anyone explain delta-epsilon method?

ptpmonitor
Our calculus teacher recently started doing limit maths using delta-epsilon method. But this method seems really complex to me and I think this method has some problem. i think sometimes we agree with un-logical decisions in order to find out the result.

|f(x)-L|<epsilon if 0<|x-a|<delta,

finally we bring,

|x-a|<epsilon/k if 0<|x-a|<delta,

and tell:

so, delta=epsilon/k

Can we tell delta=epsilon/k? Specially when it is un-equality? My madam gave some answer but that was not logical also. She told in order to find out result, we need to agree with it.

Can anyone explain this method?
guissmo
disclaimer: I just came from a Calculus course this semester. If ever I'm making a mistake, please correct me.

I'll assume you've been shown a graphical representation of this and understand what the variables f(x), L, a, x, etc mean.

Since it's an if-then statement, we need to prove that a limit L exists for f(x). To do so, we must find the case wherein the "if" part is satisfied. Why? Because if the "if" part is satisfied, then the "then" part is already true too. And so, we need to find a value for delta that satisfies the "if" part.

In what you wrote,
 Quote: finally we bring, |x-a|

You've made a series of manipulations to get to that statement.
Since epsilon/k is always greater than |x-a|<delta, then it is a good value for delta.

Therefore, delta=epsilon/k