Question

How would you prove that the limit dos not exist? I'll include the equation in the answers

Answer 1

\[\lim (x,y)->(0,0) \frac{ y }{ \sqrt{x ^{2}-y ^{2}} }\]

Answer 2

Using the two-path test

Answer 3

try going along the line x=0

Answer 4

or rather y=0

Answer 5

ok, what would the opposite direction be? If you go x = 0 you get an imaginary number

Answer 6

yeah that was my mistake, but going along y=0 the limit is...?

Answer 7

The limit is zero

Answer 8

right, now try something that is likely not to give out all zeros, for example along the line y=x-1

Answer 9

ok that worked, thank you!

Answer 10

welcome :)