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1314L22 - 1 Evaluating a function of several variables at a...

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Lesson 22 – Functions of Several Variables 1 Lesson 22 Functions of Several Variables So far, we have looked at functions of a single variable. In this section, we will consider functions of more than one variable. You are already familiar with some examples of these. y x y x P 2 2 ) , ( = t i P t i P A ) 1 ( ) , , ( + = These formulas are functions of several variables. We have just never called them that before. We will, for the most part, limit our discussion to functions of two variables. Functions of Two Variables Definition : A real valued function of two variables, f , consists of a set A of ordered pairs of real numbers ( x, y ) called the domain of the function, and a rule that associates with each ordered pair in the domain of f one and only one real number, denoted by ). , ( y x f z = You will need to learn several skills using functions of several variables:
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Unformatted text preview: 1. Evaluating a function of several variables at a given point. Example 1: Suppose . 6 4 3 ) , ( 2 +-= xy y x y x f Compute ). 3 , 1 (--f Example 2: The volume of a cylindrical tank with radius r and height h is given by the formula h r h r f V 2 ) , ( π = = . Find the volume of a tank with radius 6 feet and height 20 feet. Lesson 22 – Functions of Several Variables 2 Example 3: Find the domain of the function: . 5 2 3 ) , ( y x x y x f-= Example 4: Find the domain of the function: . 16 ) , ( 2 2 y x y x f--= Example 5: Find the domain of the function: ) 3 ln( ) , ( +-= y x y x f Example 6: Find the domain of the function: 2 2 3 2 ) , ( y x y x f + = From this section, you should be able to Evaluate a function of several variables Find the domain of a function of several variables...
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