What are the steps to solve it?

lim (x^2+y^2)/(sqrt(x^2+y^2+36)-6) as (x,y) approaches (0,0)

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  1. This one is not too nasty in the sense that x^2+y^2=r^2 when changed to polar coordinates.
    So by changing variables, you'd have

    Lim r^2/(√(r^2+36)-6)

    From here, you can multiply by the conjugate of the denominator, simplify and use the standard rules of limits to get the answer.

    You can post again if you would like to check your answer.

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