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March 28, 2017

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Use polar coordinates to find the limit. [If (r, θ) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.)
lim (x, y)→(0, 0) [(3e^−x^2− y^2) − 3]/
(x^2 + y^2)

  • calc 3 - ,

    in polar coordinates, we have

    lim (r->0) (3e^-(r^2)-3)/r^2
    = lim -6re^(-r^2))/2r
    = lim -6e^(-r^2)/2

    as r-> 0, lim = -3

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