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Calculus_MA_224_Chapter_7_Section_1 - To do this you must...

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Calculus MA 224 Chapter 7 Section 1: Functions of Several Variables Function of Two Variables : A function f of the two independent variables x and y is a rule that assigns to each ordered pair (x,y) in a given set D (the domain of f) exactly one real number, denoted by f(x,y). Domain Convention : Assume that the domain of f is the set of all (x,y) for which the expression f(x,y) is defined. Ex. 1 Suppose f(x,y) = Find domain of f Compute f(1,-2) Solution: Domain= x-y0 or xy f(1,-2)= Graphs of Functions of Two Variables : The graph of a function of two variables f(x,y) is the set of all triples (x,y,z) such that (x,y) is in the domain of f and z=f(x,y).
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Unformatted text preview: To do this, you must construct a three-dimensional graph. the xy plane is laid horizontally and z is perpendicular to this plane. To graph a function f(x,y) of the two independent variables x and y, it is customary to introduce the letter z to stand for the dependent variable and to write z=f(x,y). The ordered pairs (x,y) in the domain of f are thought of as points in the xy plane, and the function f assigns a "height" z to each such point. Thus, if f(1,2)=4, you would express this fact geometrically by plotting the point (1,2,4) in a three-dimensional space....
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