MAT 21C Lecture Notes - Lecture 19: Open Set, Level Set
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MAT 21C Full Course Notes
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Announcements: o ce hours: msb 3106 w 11/9 12-2. The set of all points (x, y, f (x, y)) in space, for (x, y) in the domain of f is called the graph of f . The graph of f is also called the surface z = f (x, y). The set of points in the plane where a function f (x, y) has a constant value f (x, y) = c is called a level curve of f . The set of points (x, y, z) in space where a function of three independent variables has a constant value f (x, y, z) = c is called a level surface of f . 14. 1. 50 f (x, y) = x2 1, (1, 0) 14. 1. 52 f (x, y) = 2y x x+y+1 , ( 1, 1) z = 0 z = 3. 14. 1. 62 f (x, y, z) = ln(x2 + y + z2), ( 1, 2, 1)
