Limit of a Multivariable functionNEED HELP

[*Helix*]

Homework Statement

Asked to find the limit of [6*(x^3)*(y^2)] / [2*(x^4) + (y^4)] as (x,y) is approaching (0,0)

Homework Equations

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

x = rcos(theta); y = rsin(theta)

The Attempt at a Solution

Tried numerous times with polar equations x = rcos(theta); y = rsin(theta)

came up with lim r -->0 [6r^2( (costheta)^3(sintheta)^2))] / [r^4(2*(costheta)^4 + (sintheta)^4]

D.N.E? ...I think its zero... can't prove it though...HELP!

 

[Billy Bob]

Welcome to PF, *Helix*.

came up with lim r -->0 [6r^2( (costheta)^3(sintheta)^2))] / [r^4(2*(costheta)^4 + (sintheta)^4]

There's your algebra error. The numerator has the wrong power of r.

 

[*Helix*]

ohh..so the function becomes : [6r(costheta)^3(sintheta)^2] /[2(costheta)^4 + (sintheta)^4] and as r is approaching zero ---> 0/(a number that will never be zero) is zero