lect12_1

lect12_1 - Functions of Several Variables - (12.1) 1....

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Functions of Several Variables - (12.1) 1. Functions of Several Variables A function of two variables, say x and y , is a relation that assigns exactly one real number to each ordered pair of real numbers x , y . A function of three variables, say x , y and z , is a relation that assigns exactly one real number to each ordered pair of real numbers x , y , z . For example, a . f ! x , y " ! 2 xy 2 b . f ! x , y , z " ! x y 2 " sin ye z The domain of a function in two variables ! x , y " is a set that contains all ordered pairs ! x , y " at which f is defined. The range of a function is the set of real numbers which are images of the function. The graph of a function of two variables is the graph of the equation z ! f ! x , y " which is a surface in space. We are not able to graph a function of three variables. Example Find and sketch the domain of the function. a . f ! x , y " ! lny 2 x 2 ! 1 b . F ! x , y , z " ! x " y xz 2 , c . G ! x , y , z " ! 36 ! 4 x 2 ! 9 y 2 ! z 2 a. f ! x , y " is defined if y # 0, and 2 x 2 ! 1 " 0, # x " $ 1
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This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.

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lect12_1 - Functions of Several Variables - (12.1) 1....

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