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Math Help - Do these 2 multivariable limits exist?

  1. #1
    Junior Member
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    Oct 2009
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    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.
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  2. #2
    Senior Member
    Joined
    Nov 2010
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    Clarksville, ARk
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    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.
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