Difference between revisions of "Math 22 Functions of Several Variables"
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==Definition of a Function of Two Variables== | ==Definition of a Function of Two Variables== | ||
| − | Let <math>D</math> be a set of ordered pairs of real numbers. If to each ordered pair <math>(x,y)</math> in <math>D</math> there corresponds a unique real number <math>f(x,y)</math>, then <math>f</math> is a function of <math>x</math> and <math>y</math>. The set <math>D</math> is the domain of <math>f</math>, and the corresponding set of values for <math>f(x,y)</math> is the range of <math>f</math>. Functions of three, four, or more variables are defined similarly. | + | Let <math>D</math> be a set of ordered pairs of real numbers. |
| + | If to each ordered pair <math>(x,y)</math> in <math>D</math> there corresponds a unique real number <math>f(x,y)</math>, then <math>f</math> is a function of <math>x</math> and <math>y</math>. | ||
| + | The set <math>D</math> is the domain of <math>f</math>, and the corresponding set of values for <math>f(x,y)</math> is the range of <math>f</math>. Functions of three, four, or more variables are defined similarly. | ||
Revision as of 06:50, 18 August 2020
Definition of a Function of Two Variables
Let be a set of ordered pairs of real numbers. If to each ordered pair in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D} there corresponds a unique real number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x,y)} , then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is a function of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} . The set Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D} is the domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} , and the corresponding set of values for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x,y)} is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} . Functions of three, four, or more variables are defined similarly.
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