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Expert: - 10/28/2009


Question
Can you help me with an epsilon delta proof of two variables?
I need to prove the limit of cos(xy) as f(x,y) --> (1,pi/2)


Answer
Can you help me with an epsilon delta proof of two variables?
I need to prove the limit of cos(xy) as f(x,y) --> (1,pi/2)

I think there is a theorem that if cos(xy) --> cos(pi/2) = 0 from the x-direction AND from the y-direction, that should do it.

So try to prove that (in the x-direction, y = pi/2):

| cos (pi/2 x) - cos (pi/2) | < epsilon

and that (in the y-direction, x = 1):

| cos (y) - cos (pi/2) | < epsilon  

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