In my calculus book it says that the limit of y(x^3) as (x,y)->(0,1) equals 0. It also says that a limit does not exist if you obtain different values when approaching (0,1) from different paths.(adsbygoogle = window.adsbygoogle || []).push({});

It is easy to see the limit is zero by using the product rule for limits. However, if I set x=y, we get the limit of x^4 as (x,y)->(0,1) or the limit of y^4 as (x,y)->(0,1) which are clearly not equal. Hence the limit does not exist (?).

Where is my reasoning false?

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# Limit, two variables

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