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Homework Help: Limit of a Multivariable functionNEED HELP!

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

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

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

    3. 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!!!
  2. jcsd
  3. Oct 2, 2009 #2
    Welcome to PF, *Helix*.

    There's your algebra error. The numerator has the wrong power of r.
  4. Oct 2, 2009 #3
    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
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