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Unformatted text preview: FUNCTIONS OF TWO VARIABLES Math21a, O. Knill HOMEWORK: Section 12.4: 10, 46 and Section 13.1: 38, 46, 64 FUNCTIONS, DOMAIN, RANGE AND GRAPH. We deal with functions f ( x, y ) of two variables defined on a domain D in the plane. The domain is usually the entire plane like for f ( x, y ) = x 2 + sin( xy ). But there are cases like f ( x, y ) = 1 / radicalbig 1- ( x 2 + y 2 ), where the domain is a subset of the plane. The range of f is the set of possible values of f . The graph of f is the set { ( x, y, f ( x, y )) | ( x, y ) ∈ D } . EXAMPLES. function f ( x, y ) domain D range f ( D ) f ( x, y ) = sin(3 x + 3 y )- log(1- x 2- y 2 ) open unit disc x 2 + y 2 < 1 [- 1 , ∞ ) f ( x, y ) = f ( x, y ) = x 2 + y 3- xy + cos( xy ) entire plane R 2 entire real line f ( x, y ) = radicalbig 4- x 2- 2 y 2 closed elliptic region x 2 + 2 y 2 ≤ 4 [0 , 2] f ( x, y ) = 1 / ( x 2 + y 2- 1) everything but the unit circle entire real line f ( x, y ) = 1 / ( x 2 + y 2 ) 2 everything but the origin positive real axis LEVEL CURVES If f ( x, y ) is a function of two variables, then f ( x, y ) = c = const is a...
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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