Lecture 12-1

# Lecture 12-1 - in the plane where Example Identify and...

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12.1 Functions of Several Variables One-Variable Functions The statement ” y = f ( x ) 00 or ” y is a function of x ” means y depends on x . x = y = Domain = In words: Range = In words: 1

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Two-Variable Functions z = f ( x, y ) or ” z is a function of x and y ” means z depends on BOTH x and y . x, y = z = Domain = Range = Three or More Variables w = f ( x, y, z ) x, y, z = w = 2
Example Find the domain and range of the following functions. Sketch the domain. 1. f ( x, y ) = y 2 - x 2 2. f ( x, y ) = tan - 1( x y ) 3. f ( x, y ) = p x 2 + y 4. z = ln ( 9 - ( x 2 + y 2 ) ) 3

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Tips To ﬁnd domain: 1. 2. To ﬁnd range: 1. 2. 4
Level Curves Defn. Level Curve A level curve (or contour) for a function z = f ( x, y ) is the set of all points

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Unformatted text preview: in the plane where Example Identify and graph the level curves of the following functions. 1. f ( x, y ) = p x 2 + y 2 2. f ( x, y ) = y x 2 5 Note: 1. 2. 3. What do you think the level curves of the following functions will look like? 1. x 2 + y 2 4 + z 2 = 1 2. z = y 2 6 Do. 1. Find the domain and range of the following functions. Sketch the domain. a) f ( x, y ) = x-y x + y b) f ( x, y ) = ln( x + y-1) 2. Graph f ( x, y ) = cos y . 7...
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## This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Lecture 12-1 - in the plane where Example Identify and...

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