Vector function- limits HELP?

• Apr 19th 2013, 08:58 PM
prosri29
Vector function- limits HELP?
HI guys
Question:

Consider the function
f(x,y) =x^(3)y/(x^(6) + y^(2)) .

(c) Does lim(x,y)-->(0,0) f(x,y) exist? If so, what is its value?

I need to solve using limits definition:

sqt((x-a)^2 + (y-b)^2 )< d such that l f(x,y) - L l < e
• Apr 19th 2013, 10:31 PM
chiro
Re: Vector function- limits HELP?
Hey prosri29.

Hint: You should get an answer that the limit does not exist since lim x->0,y=0 != lim y->0,x=0.
• Apr 19th 2013, 10:47 PM
prosri29
Re: Vector function- limits HELP?
Hey chiro

I have already proved as x=0 y--->0 and as y=o x----->0 therefore limit exists and is 0.

But I no need to determine whether a limit exists using the limit definition
• Apr 20th 2013, 12:13 AM
chiro
Re: Vector function- limits HELP?
I haven't done this kind of thing for a while so unfortunately I can't help with epsilon delta stuff.
• Apr 20th 2013, 12:22 AM
prosri29
Re: Vector function- limits HELP?
no worries thanks for your suggestions