Question

I need help with "The Definition of the Limit". I don't understand how to prove a problem

Answer 1

what problem?

Answer 2

epsilon-delta definition?

Answer 3

Yes

Answer 4

Definition of the Limit is:
\[\lim_{x \rightarrow c}f(x)=L\]
ƒ is a function and ƒ(x) can be made as close as desired to L by making the independent variable x close enough, but not equal, to the value c.

The (ε, δ)-definition of the limit of a function is as follows:
\[\lim_{x \rightarrow c}f(x)=L\]
ƒ is a function defined on an open interval containing c (except possibly at c) and let L be a real number.
It means for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |ƒ(x) − L| < ε,
or, symbolically, \[\forall \epsilon>0, \exists \delta>0: \forall x (0<|x − c| < δ =>|ƒ(x) − L| < ε)\]

Answer 5

unless you are in an analysis class, do not try and understand, at length, the definition of a limit. What are you having problems with.