Infinite Limits - Vertical Asymptotes

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In this video I go over infinite limits and what vertical asymptotes are in detail. In my earlier videos I have covered infinite limits and vertical asymptotes but have not gone in too much detail as I did in this video so make sure to watch this video!


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Infinite Limits: Vertical Asymptotes

Infinite Limits Vertical Asymptotes.JPG

Vertical Asymptotes

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Definition:

Let f be a function defined on both sides of a, except possibly at a itself.

Then:

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Means that the values of f(x) can be made arbitrarily large (as large as we please) by taking x sufficiently close to a, but not equal to a.

Limit does not exist
The infinite symbol (∞) is not a number
It is used to describe how the limit does not exist
“The limit of f(x), as x approaches a, is infinity”
The vertical line x = a is called a Vertical Asymptote

Similarly for Negative infinity limits:

image.png

One Sided Limits:

image.png

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