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lecture5 - Lecture 5: Multivariable Functions May 12, 2009...

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Lecture 5: Multivariable Functions May 12, 2009 Lecture 5: Multivariable Functions
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Objectives 1 Extend definition of single variable function 2 Find the domain and range of multivariable functions 3 Recognize graphs of multivariable functions 4 Draw level curves of multivariable functions 5 Extend ideas of limits and continuity. Lecture 5: Multivariable Functions
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Multivariable functions A function of two variables is a rule that assigns to each ordered pair of numbers ( x , y ), a unique real number f ( x , y ). Two inputs: x and y called independent variables. One output z= f ( x , y ) called the dependent variable. Physical examples: 1 Temperature of surface of an ocean at some fixed time longitude and latitude 2 Altitude of the surface of the earth depends on longitude and latitude 3 The area of a right triangle depends on the length of its two legs. Lecture 5: Multivariable Functions
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Domain of a function f ( x , y ) is the set of allowable ( x
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lecture5 - Lecture 5: Multivariable Functions May 12, 2009...

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