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I was introduced to functions of more than one variable today and how to work out limits with them. My teacher said that to check if a limit exists you should approach the point from a few directions and if the limit from any of these directions change then the limit doesn't exist. So my question is does the two points need to lie on the line that you would choose to approach it from(so if I had to approach the point $(2,1)$ could I use the equation $y=x$ and substitute that into the function or would I need to choose the equation $2y=x$ or $y=x-1$)? Many thanks

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    You must have $y(2)=1$ or $x(1)=2$. Else, how would you approach the point in interest? – 2017-01-30
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    Ok so I need to choose an equation of a line to sub in that both points would lie on? – 2017-01-30
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    Yes, you need that. – 2017-01-30

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