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MATH 151 Lecture Notes - Lecture 9: Partial Derivative, Level Set, Contour Line

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rosebutterfly429

6 May 2016

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Simon Fraser University

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In many practical situations, the formulation of a problem results in a mathematical model that involves a function of two or more variables. The variables x and y are called independent variables and z = f (x, y) is called dependent variable. Let f be the function de ned by f (x, y) := x + xy + y2 + 2. Compute f (0, 0), f (1, 2) and f (2, 1). Note that f (1, 2) 6= f (2, 1). Find the domain of each of the following functions: (a) f (x, y) = 2x + 3y; (b) f (x, y) = xy x y ; (c) f (x, y) =p4 x2 y2. Solution: (x, y) in the domain of f if and only if f (x, y) is de ned. 1 (a) f (x, y) = 2x + 3y is well-de ned for any real numbers x and y.

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