Quiz3_sol - z = e xe y . (2 points) Solution . Since z = e...

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NAME: Spring 2011, MAC 2313, Quiz 3 UFID: Section: 3124 1. Determine the set of points at which the function y x 2 - y 2 + z 2 is continuous. (2 points) Solution . y x 2 - y 2 + z 2 has natual domian D = { ( x,y ) : y 0 ,x 2 - y 2 + z 2 6 = 0 } , in which both y and x 2 - y 2 + z 2 are continuous, and x 2 - y 2 + z 2 6 = 0. So the set is D . 2. Find the partial derivative 3 z ∂u∂v∂w where z = u v - w . (2 points) Solution . Since z = u v - w , we have ∂z ∂w = - u 2 v - w 2 z ∂v∂w = u 4( v - w ) 3 3 z ∂u∂v∂w = 1 4( v - w ) 3 (1) 3. Find all the second order partial derivatives of
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Unformatted text preview: z = e xe y . (2 points) Solution . Since z = e xe y , we have z x = e xe y e y = e xe y + y z y = e xe y xe y = xe xe y + y 2 z x 2 = e xe y + y e y = e xe y +2 y 2 z yx = e xe y + y ( xe y + 1) 2 z xy = e xe y + y + e xe y + y xe y = e xe y + y ( xe y + 1) 2 z y 2 = xe xe y + y ( xe y + 1) (2)...
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