Calc 3

Find the limit, if it exists. (If an answer does not exist, enter DNE.)
lim (x, y)→(0, 0)
of (x^2 + y^2)/[((x^2 + y^2 +64)^.5)-8]

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  1. one good way to tackle xy limits is to convert to polar coordinates, then let r->0

    f(r,theta) = r^2/(sqrt(r^2+64)-8)

    now, using lHospital's Rule,

    lim = 2r/[2r/(2sqrt(r^2+64))]
    = 2sqrt(r^2+64))
    = 2*8 = 16

    Since the function does not involve theta, the limit is the same from all directions.

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  2. but there is no lHospitals rule in multivariable

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