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# Day-9-filled - Math 1314 Day 9 Functions of Several...

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Math 1314 Day 9 Functions of Several Variables Section 16.1 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: 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 ( and ) 1 , 2 ( ), 0 , 0 ( - - - f f f

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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.
Example 3: Suppose you borrow money to buy a house. You agree to a 30-year loan with equal payments. This formula gives the amount of the reduction in principal of the loan (given in dollars) after making i payments on a loan of A dollars amortized over t years.

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