- #1

ek124

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- TL;DR Summary
- how to show a multivariable limit does not exist/exist

I want to show that the limit of the following exists or does not exist:

When going along the path x=0 the limit will tend to 0 thus if the limit exists it will be approaching the value 0

when going along the path y=0, we get an equation with divisibility by zero. Since this is not possible does this already show that the limit does not exist? Or does it simply mean that there is an asymptote... I would like to know what this means.

Finally when going along the path y=x^2, the limit tends to 1. Since the first and last path give a different outcome the limit DNE however I want to know what the path along y=0 tells us anyway.

When going along the path x=0 the limit will tend to 0 thus if the limit exists it will be approaching the value 0

when going along the path y=0, we get an equation with divisibility by zero. Since this is not possible does this already show that the limit does not exist? Or does it simply mean that there is an asymptote... I would like to know what this means.

Finally when going along the path y=x^2, the limit tends to 1. Since the first and last path give a different outcome the limit DNE however I want to know what the path along y=0 tells us anyway.