Precise Definition of Limits at Infinity - Horizontal Asymptotes

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In this video I go over precise definition of a limit at infinity and negative infinity. Like my previous video on the precise definition of a limit, the concept is somewhat abstract but if you go over the video carefully, the definition is pretty straight forward.


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Precise Definition of Limits at Infinity – Horizontal Asymptotes

Precise Definition of Limits at Infinity.jpg

Definition:

Let f be a function defined on some interval (a,∞). Then:

image.png

Means that for every ε > 0 there is a corresponding N such that:

image.png

Let’s choose a smaller ε.

image.png


Similarly for limits at negative infinity:

Definition:

Let f be a function defined on some interval (-∞,a). Then:

image.png

Means that for every ε > 0 there is a corresponding N such that:

image.png



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