Question

Evaluate:
lim (x,y)->(0,0) of (xy^2)/(x^2+y^2)^(3/2)

Answer 1

\[\lim_{(x,y)\rightarrow 0} \frac{ xy^2 }{ (x^2+y^2)^{3/2} }\]
Do you mean this?

Answer 2

I'm sure he means \[\lim_{(x,y)\rightarrow (0,0)} \frac{ xy^2 }{ (x^2+y^2)^{3/2} }\]

Answer 3

@Zarkon Correct! Just as a side note how do you write equations when asking a question (I know how to do it in replies)

Answer 4

I think it works the same way in the questions as it does in replies, it's just that replies doesn't give you an equation editor.

Answer 5

i am still in single var i'll try
\[\frac{ xy^2 }{ (r^2) ^{3/2}}\]
\[\frac{ xy^2 }{ r^3 }=\frac{ r^3\sin ^2\theta \cos \theta }{ r^3}=\cos \theta-\cos^3\theta\]

Answer 6

1-1^3=0

Answer 7

\[r \cos \theta \rightarrow 0\]

Answer 8

are you assuming \(\theta=0\)?