Questions from General Calculus


Q: Use traces to sketch and identify the surface. 9y2 +

Use traces to sketch and identify the surface. 9y2 + 4z2 = x2 1 36

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Q: Use traces to sketch and identify the surface. 3x2 +

Use traces to sketch and identify the surface. 3x2 + y + 3z2 = 0

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Q: Use traces to sketch and identify the surface. 3x2 -

Use traces to sketch and identify the surface. 3x2 - y2 + 3z2 = 0

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Q: Use traces to sketch and identify the surface. y =

Use traces to sketch and identify the surface. y = z2 - x2

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Q: Use traces to sketch and identify the surface.x =

Use traces to sketch and identify the surface. x = y2 - z2  

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Q: Sketch the graph of a function that satisfies the given conditions.

Sketch the graph of a function that satisfies the given conditions. f (0) = 0, f ‘(-2) = f ‘(1) = f ‘(9) = 0,

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Q: A cooling tower for a nuclear reactor is to be constructed in

A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet (see the photo on page 839). The diameter at the base is 280 m and the minimum diameter, 500 m abo...

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Q: Show that if the point (a, b, c)

Show that if the point (a, b, c) lies on the hyperbolic paraboloid z = y2 - x2, then the lines with parametric equations x = a + t, y = b + t, z = c + 2 (b 0- a) t and x = a + t, y = b - t, z = c – 2...

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Q: Show that the curve of intersection of the surfaces x2 + 2y2

Show that the curve of intersection of the surfaces x2 + 2y2 - z2 + 3x = 1 and 2x2 + 4y2 - 2z2 - 5y = 0 lies in a plane.

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Q: (a). What does the equation y = x2 represent as

(a). What does the equation y = x2 represent as a curve in R2? (b). What does it represent as a surface in R3? (c). What does the equation z = y2 represent?

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