quiz5soln

Quiz5soln - approaches(0 0 along the following paths 1 x = x y = 0 z = 0 and 2 x = 0 y = y z = 0 1 Setting y = z = 0 We have lim x → x 2 x 2 =

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MATH 231 / Spring 2008 February 20, 2008 Name: Key 1. (3 points) Match the following functions with their graphs. (a) z = sin( xy ) (b) z = sin( x - y ) (c) z = sin x - sin y (1) (2) (3) Solution: (a) = (1) , (b) = (2) , (c) = (3) . 2. (7 points) Find the limit, if it exists, or show that the limit does not exist. lim ( x,y,z ) (0 , 0 , 0) x 2 + 2 y 2 + 3 z 2 x 2 + y 2 + z 2 Solution: We will prove that this limit does not exist. To do so, we will look at the limit of the function as it
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Unformatted text preview: approaches (0 , , 0) along the following paths: 1: x = x, y = 0 , z = 0 and 2: x = 0 , y = y, z = 0. 1: Setting y = z = 0, We have lim x → x 2 x 2 = lim x → 1 = 1 2: Let’s set x = z = 0. Then we get lim y → 2 y 2 y 2 = lim y → 2 = 2 Since these two values are not equal, the limit does not exist. 1...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.

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