Precise Definition of One Sided Limits

in MES Science2 months ago

In my earlier videos I went over how to precisely define and prove the limits of a function in general. In this video I use the same concept but look at one sided limits and how to precisely define them. The concept is pretty much the same as for general limits.


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Precise Definition of One Sided Limits

Precise Definition of One Sided Limits.jpg

Recap Intuitive Definition

Left Hand Limit:

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“The limit of f(x) as x approaches a from the left is equal to L”

Right Hand Limit:

“The limit of f(x) as x approaches a from the right is equal to L”

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Precise Definition of Left Hand Limit

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If for every number ε>0 there is a number δ>0 such that:

image.png

Precise Definition of Right Hand Limit

image.png

If for every number ε>0 there is a number δ>0 such that:

image.png

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