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Engineering Calculus Notes 414

Engineering Calculus Notes 414 - of bowl shape known as an...

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402 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION which is a parabola opening up from the origin, while the intersection with the yz -plane ( x = 0) has equation z = y 2 which also opens up from the origin, but is twice as “broad”(see Figure 3.34 ). x y z Figure 3.34: Intersection with vertical planes Fitting these pictures together, we see that the surface is a kind
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Unformatted text preview: of bowl shape, known as an elliptic paraboloid (Figure 3.35 ). x y z Figure 3.35: Elliptic Paraboloid 4 x 2 + y 2 − z = 0 (c) If both x and y appear squared, and their coe±cients have opposite signs, then our level sets are hyperbolas centered at the...
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