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Math Help - multivariable limit with 3 vars!

  1. #1
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    multivariable limit with 3 vars!

    ok i got alright at the limits with two variables (to an extent haha)

    but now i have this limit:

    lim (x,y,z) --> (0,0,0) of (2(x^2)ycos(z))/(x^2 + y^2)

    where do i start?
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  2. #2
    MHF Contributor chisigma's Avatar
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    The variable z is only in the term \cos z that is equal to 1 for z=0, so that the 'real' limit is...

    \displaystyle \lim_{(x,y) \rightarrow (0,0)} \frac{2\ x^{2}\ y}{x^{2} + y^{2}}

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by BrianMath View Post
    ok i got alright at the limits with two variables (to an extent haha)

    but now i have this limit:

    lim (x,y,z) --> (0,0,0) of (2(x^2)ycos(z))/(x^2 + y^2)

    where do i start?
    Never mind.
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  4. #4
    Super Member General's Avatar
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    \left| \dfrac{2x^2ycos(z)}{x^2+y^2} \right| \leq 2y

    Use sandwich.
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