Thread: Do these 2 multivariable limits exist?

1. Do these 2 multivariable limits exist?

Sorry, I haven't done this in a while and I just would like to double check if the following 2 limits exist or do not exist. A short explanation would be very helpful.

#1 lim(x,y)-->(0,0) of (x^3*y^2)/(x^2 + y^4)

#2 lim(x,y)-->(0,0) of (x^3*y^2)/(x^6 + y^4)

Thanks a lot. Much appreciated.

2. Re: Do these 2 multivariable limits exist?

The first one, $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^2 + y^4}\,,$ exists.

The second one, $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^6 + y^4}\,,$ Does Not Exist.

It's helpful to express them in polar coordinates to see this.