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Extra Practice Problems

Extra Practice Problems - Math 1920 Prelim I Practice...

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Math 1920, Prelim I Practice Problems 1. Suppose that f ( x, y ) is a function defined and continuous everywhere in the plane except at (0 , 0). The figure shows some of the distinct level curves as solid circles tangent to the x -axis at the origin. Suppose further that lim y 0 f (0 , y ) = 0 = lim x 0 f ( x, 0). Does lim ( x,y ) (0 , 0) f ( x, y ) exist? Does lim x 0 f ( x, kx ) = 0 for all k ? f(x,y) = 1 y x 2. Is there a non-zero value of the number
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