Question

Find the limit if it exists. If the limit does not exist, then find two paths in the xy- plane that produce different limits in order to verify that it doesn’t exist.
lim (3x^(2))/(x^(4)+ y^(2))
(x,y)-> (0,0)

Please explain step by step

Answer 1

\[\lim_{x \rightarrow y} 3x ^{2}y \div x ^{4} + y ^{2}\]

Answer 2

i meant (x,y) -> (0,0) under the limit

Answer 3

one of the cool tricks I use for finding multi dimensional limits is to convert to polar

x= r sin theta
y= r cos thata

And
limit becomes as r approaches 0 it usually works

Answer 4

I have to find two different paths to prove it does not exist and i dont know how to do that

Answer 5

basically the limit doesn't exist when you get 2 different results from 2 different paths

Answer 6

i understand that i just am not sure how to do it

Answer 7

Just plug in different values use

f(0,x)
f(0,x^2)
f(0,x^3)

And such until you find 2 f(x,y) that dont equal same then those are you 2 ...