Question

lim(x,y)→(0,0)2x^2y/x4+y4

Answer 1

is this your question\[\lim\limits_{x\rightarrow 0}\lim\limits_{y\rightarrow 0} \frac{2x^2y}{x^4+y^4}\]

Answer 2

\[\small\text{\[\lim\limits_{x\rightarrow 0}\lim\limits_{y\rightarrow 0} \frac{2x^2y}{x^4+y^4}\]}\]

Answer 3

\[\lim\limits_{(x,y)\rightarrow (0,0)} \frac{2x^2y}{x^4+y^4}\]

Answer 4

have i got the question right now/

Answer 5

i dont really know how to answer this question sorry ,
my guess is that it asymptotes at the origin

Answer 6

The value of limit does not exist

Answer 7

yes, one way i know is to put \(r= \sqrt{x^2+y^2}\)and r= x cos t, r= y sin t
so put, x^2 = r^2/cos^2 t ,
\(x^4+y^4 = (x^4+y^4-2x^2y^2+2x^2y^2) = (x^2+y^2)^2-2x^2y^2\)
substituting all these we get r in denominator(as r^3 gets cancelled) and functions of t in both numerator and denominator .......and as r->0 , the limit tends to infinite irrespective of what t tends to..