2224Test1Review

2224Test1Review - MATH 2224: PRACTICE PROBLEMS FOR TEST #1...

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MATH 2224: PRACTICE PROBLEMS FOR TEST #1 1. Completely describe each surface and plot each surface in 3-space. (a) 8 z y x 2 = + + (b) 16 z x 2 2 = + (c) 0 z y x 2 2 2 = + + (d) 1 z 9 y 4 x 2 2 2 = + + (e) 4 z y x 2 2 2 = + 2. For each of the following, find the limit or show that it does not exist. (a) y x y 2 x lim 2 ) 0 , 0 ( ) y , x ( + + (b) 2 2 2 ) 0 , 0 ( ) y , x ( y x xy lim + 3. If z ln y e x ) z , y , x ( w yz 2 + = , find x w , xy w , and z w . 4. Use the chain rule to find s w if 2 2 y x w + = , t cos s x = , and t sin s y = . Simplify your answer. 5. Use the chain rule to find r w and s w when r = π and s = 0 if w = sin(2x - y), x = 4 + sin s, and y = rs. 6. On an xy-coordinate plane, sketch the domain of each of the following functions. Use a dotted boundary to indicate the boundary points are NOT included and a solid boundary to indicate the boundary points are included. Tell whether the domains are (i) bounded or unbounded; (ii) open, closed, or neither. (a) 2 2 y x 9 1 ) y , x ( f z = = (b) ) y x ln( ) y , x ( f z 2 + = = (c) 2 2 y x 4 4 1 ) y , x ( f z = = (d) 2 2 y x ) y , x ( f z = = 7. By considering different paths of approach, show that the following limit does not exist:: (a) 2 2 ) 0 , 0 ( ) y , x ( y
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This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224Test1Review - MATH 2224: PRACTICE PROBLEMS FOR TEST #1...

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