functions_of_two_variables

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F unctions of T wo V ariables Up until this point, we have studied functions that take in a single input and produce a single output. Often times in everyday life, quantities depend on more than one variable. For example, the body mass index (BMI) that is often used to classify whether or not a person is overweight is given by the formula 2 Weight (in pounds) BMI 703 [Height (in inches)]  If we were to let x denote a person’s weight (in pounds), y denote a person’s height (in inches), and z denote their BMI, then we would have 2 ( , ) 703 x zf x y y  . In this case, we say that f ( x , y ) is a function of two inputs (variables) . The independent variables are x and y and z is the dependent variable . That is, the output z (in this case, BMI) depends on the inputs x and y (weight and height). A natural question is how to convey the information of such a function. When we had only a single input and a single output, we could make a one-dimensional table of values and we could plot the result in two dimensions. Now, with two inputs, we require a two- dimensional table of values and plot the result in three dimensions. Below is a table of some BMI values. Weight (lbs) 110 120 130 140 150 160 170 180 190 5'4" 18 20 22 24 25 27 29 31 32 5'5" 18 20 21 23 25 26 28 30 31 5'6" 17 19 21 22 24 25 27 29 30 Height 5'7" 17 18 20 22 23 25 26 28 29 (in) 5'8" 16 18 19 21 22 24 25 27 28 5'9" 16 17 19 20 22 23 25 26 28 5'10" 15 17 18 20 21 23 24 25 27 5 ' 1 1 " 1 51 61 81 92 12 22 32 52 6 6'0" 14 16 17 19 20 21 23 24 25
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This note was uploaded on 09/07/2011 for the course MATH 10C taught by Professor Hohnhold during the Spring '07 term at UCSD.

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functions_of_two_variables - Functions of Two Variables Up...

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