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Engineering Calculus Notes 279

# Engineering Calculus Notes 279 - f x,y we consider the...

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3.4. LEVEL CURVES 267 x y a z = a 2 : x 2 + y 2 = a 2 y z x = 0 : y 2 = z y z x Figure 3.4: Slicing the Surface x 2 + y 2 = z centered at the origin, with major axis along the y -axis and minor axis along the x -axis. L ( f,a 2 ) again crosses the y -axis at the pair of points (0 , ± a ), and it crosses the x -axis at the pair of points ( ± a/ 2 , 0). To see how these ellipses fit together to form the graph of
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Unformatted text preview: f ( x,y ), we consider the intersection of the graph z = 4 x 2 + y 2 with the yz-plane x = 0; the intersection is found by substituting the second equation in the ±rst to get the parabola z = y 2 . Similarly, the intersection of the graph with the xz-plane y = 0...
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