Unformatted text preview: functions, the level sets really are curves. For example (see Figure 3.1 : • The level curves of a nonconstant a±ne function are parallel straight lines. • The level curves of the function f ( x,y ) = x 2 + y 2 are concentric circles centered at the origin for c > 0, just the origin for c = 0, and the empty set for c < 0. • For the function f ( x,y ) = x 2 4 + y 2 the level sets L ( f,c ) for c > 0 are the ellipses centered at the origin x 2 4 c 2 + y 2 c 2 = 1 which all have the same eccentricity. For c = 0, we again get just the origin, and for c < 0 the empty set. • The level curves of the function f ( x,y ) = x 2 − y 2 are hyperbolas:...
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 Fall '08
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 Calculus, Level set

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