lecture05

lecture05 - Lecture 5 Ch14 Function of two or more...

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2006 Fall MATH 100 Lecture 4 1 Lecture 5 Ch14 Function of two or more variables 123 1 Examples, A 2 V 1 ( ... ) Standard notations: ( , ) n bh lwh Xx x x x n zf x y = = =+ + + + = ( , , ) ( , , ,.... ) n wf x y z uf x x x x = =
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2006 Fall MATH 100 Lecture 4 2 Lecture 5 Ch14 Function of two or more variables 12 n n Definition: A function of variables , ,..., is a rule that assigns a unique number to each point ( , ,..., ) in some set of dimensional space. : Domain where a function is defined. Def fn x x x fx x x Dn D ault domain: all real number excluding where the function is not defined.
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2006 Fall MATH 100 Lecture 4 3 Lecture 5 Ch14 Function of two or more variables 0 : Sol ? ) ln( of domain : Ex . } 0 | , {( or 0 domain Natural 1 ) ( 9 1 9 ) ( 3 ) 9 , ( 5 1 4 1 3 ) 4 , 1 ( Clearly, . 1 3 ) , ( : Ex 2 2 2 2 2 2 > = = = = = = y x y x f(x,y) y y x y b ab b ab b ab f f y x y x f
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2006 Fall MATH 100 Lecture 4 4 Lecture 5 Ch14 Function of two or more variables 22 2 Graph of function in 2-space Ex: Graph of 1 (1) ( , ) 1 is just the graph for 2 11 1 or 1 (2) ( , ) 1 ? 1, 0. fxy x y Zx y x y z x y xyz z =−− + + = =− ++=
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2006 Fall MATH 100 Lecture 4 5 Lecture 5 Ch14 Function of two or more variables 22 222 (3) ( , ) is just the graph for , 0. (2) ( , ) 1 ? 1, 0. fxy x y zxy z xyz z =− + =+ ++=
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2006 Fall MATH 100 Lecture 4 6 Lecture 5 Ch14 Function of two or more variables k y x f k k z y x f z height of curve level - - - ) , ( in results by Cut ) , ( elevation? constant of curves Contour : EX functions of tion representa Geometric : curve Level = = = k z =
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lecture05 - Lecture 5 Ch14 Function of two or more...

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