Definition for the limit as x->infinity

[felvt]

I am supposed to construct a definition for the statement lim of f(x) as x goes to infinity = L. Then use that constructed definition to prove that the lim(1/x) as x goes to infinity = 0.

I believe the definition is supposed to resemble the epsilon-delta definition for functional limits, but I am not sure how it applies to the case where x goes to infinity.

 

[mmm4444bot]

Hello Felvt:

If you understand the epsilon-delta definition for the limit as x approaches a, then you understand how it explains the statement, "We can make the value of f(x) arbitrarily close to L by taking x to be sufficiently close to a".

For limits at infinity, think about the statement, "We can make the value of f(x) arbitrarily close to L by taking x to be sufficiently larger than A."

Here, A is a value between zero and infinity, and it depends on epsilon just as delta depends on epsilon.

Did you draw a picture?

Cheers,

~ Mark