14.1-14.2solns

# 14.1-14.2solns - x y = y csc x(d f x y = sin x 2 y 2...

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MATH 231 Group Work Quiz Related 1. Find and sketch the domains of the following functions: (a) f ( x, y ) = x + y (b) f ( x, y ) = x + y (c) f ( x, y ) = x - ln( y - x ) Answers: (a) -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1 1 2 (b) -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1 1 2 (c) -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1 1 2 2. Compute the limits or explain why they don’t exist. 1

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(a) lim ( x,y ) (0 , 0) x 4 - y 4 x 2 + y 2 (b) lim ( x,y ) (0 , 0) 6 x 3 y 2 x 4 + y 4 (c) lim ( x,y ) (1 , - 1) e - x 2 y sin( x + y ) (d) lim ( x,y,z ) (0 , 0 , 0) xy + yz 2 + xz 2 x 2 + y 2 + z 4 Answers: (a) 0. Removable discontinuity. (b) DNE. Look at y = 0 and y = x . (c) 0. Just evaluate. Continuity gives it to you. (d) DNE. Look at x = y = z 2 and y = z = 0. 3. Roughly sketch the contour map for the following functions: (a) f ( x, y ) = x 2 + ( y + 1) 2 (b) f ( x, y ) = ye x (c) f (

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Unformatted text preview: x, y ) = y csc x (d) f ( x, y ) = sin( x 2 + y 2 ) Answers: (a)-5-4-3-2-1 1 2 3 4 5-2-1 1 2 2 (b)-5-4-3-2-1 1 2 3 4 5-2-1 1 2 (c) (bad things happen at π )-5-4-3-2-1 1 2 3 4 5-2-1 1 2 (d)-5-4-3-2-1 1 2 3 4 5-2-1 1 2 4. Evaluate the following limits using polar coordinates. (a) lim ( x,y ) → (0 , 0) x 4-y 4 x 2 + y 2 (b) lim ( x,y ) → (0 , 0) x 2 x 2 + y 2 (c) lim ( x,y ) → (0 , 0) x 3-y 3 x 2 + y 2 3 Answers: (a) 0. (b) DNE. Changes as θ changes. (c) 0. 4...
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14.1-14.2solns - x y = y csc x(d f x y = sin x 2 y 2...

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