14.1-14.2

# 14.1-14.2 - y 1 2(b f x,y = ye x(c f x,y = y csc x(d f x,y...

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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 ) 2. Compute the limits or explain why they don’t exist. (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 3. Roughly sketch the contour map for the following functions: (a) f ( x, y ) =
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Unformatted text preview: y + 1) 2 (b) f ( x,y ) = ye x (c) f ( x,y ) = y csc x (d) f ( x,y ) = sin( x 2 + y 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 1...
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