Questions from General Calculus


Q: Differentiate the function. y = 1 / ln x

Differentiate the function. y = 1 / ln x

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Q: (a). Sketch the graph of y = ex as a

(a). Sketch the graph of y = ex as a curve in R2. (b). Sketch the graph of y = ex as a surface in R3. (c). Describe and sketch the surface z = ey.

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Q: Suppose that u ∙ (v × w) = 2.

Suppose that u ∙ (v × w) = 2. Find (a). (u × v) ∙ w (b). u ∙ (w × v) (c). v ∙ (u × w) (d). (u × v) ∙ v

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Q: Show that if a, b, and c are in V3

Show that if a, b, and c are in V3, then (a × b) ∙ [(b × c) × (c × a) g = [a ∙ (b × c)]2

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Q: Find the acute angle between two diagonals of a cube.

Find the acute angle between two diagonals of a cube.

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Q: A boat is pulled onto shore using two ropes, as shown

A boat is pulled onto shore using two ropes, as shown in the diagram. If a force of 255 N is needed, find the magnitude of the force in each rope.

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Q: Reduce the equation to one of the standard forms, classify the

Reduce the equation to one of the standard forms, classify the surface, and sketch it. x2 - y2 - z2 - 4x - 2z + 3 = 0

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Q: Find an equation of the plane. The plane through (

Find an equation of the plane. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1)

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Q: Find an equation of the plane. The plane through (

Find an equation of the plane. The plane through (1, 2, -2) that contains the line x = 2t, y = 3 - t, z = 1 + 3t

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Q: Find the point in which the line with parametric equations x =

Find the point in which the line with parametric equations x = 2 - t, y = 1 + 3t, z = 4t intersects the plane 2x - y + z = 2.

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