Proving that a limit of a two-variable function does not exist

  • #1
Find the limit as (x,y) -> (0,0) of (x^4 + y^4)/(x^3 + y^3)

This was a question from a recent homework set (class homework is done online), and the server accepted 0 as an answer. However, the actual answer is that the limit does not exist. My professor told us this afterwards and proposed that we find a way to prove that the limit indeed does not exist (I'm assuming this means to find a function from which the limit does not approach 0). But every function I have tried so far ends up making the limit 0.

Anyone up for a challenge? :)
 

Answers and Replies

  • #2
Avodyne
Science Advisor
1,396
88
Consider the line y=bx. Can you find a value of b such that the function blows up at all nonzero values of x on this line?
 

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