Questions from General Calculus


Q: Write equations in standard form of the six types of quadric surfaces

Write equations in standard form of the six types of quadric surfaces.

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Q: Use Stokes’ Theorem to evaluate ∫∫S curl F ∙ dS

Use Stokes’ Theorem to evaluate ∫∫S curl F ∙ dS, where F (x, y, z) = x2yz i + yz2 j + z3exy k, S is the part of the sphere x2 + y2 + z2 = 5 that lies above the plane z = 1, and S is oriented upward....

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Q: How do you add two vectors geometrically? How do you add

How do you add two vectors geometrically? How do you add them algebraically?

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Q: How do you find the vector from one point to another?

How do you find the vector from one point to another?

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Q: How do you find the dot product a ∙ b of two

How do you find the dot product a ∙ b of two vectors if you know their lengths and the angle between them? What if you know their components?

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Q: Write expressions for the scalar and vector projections of b onto a

Write expressions for the scalar and vector projections of b onto a. Illustrate with diagrams.

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Q: How do you find the cross product a × b of two

How do you find the cross product a × b of two vectors if you know their lengths and the angle between them? What if you know their components?

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Q: Use power series to solve the differential equation. y' –

Use power series to solve the differential equation. y' – y = 0

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Q: Solve the differential equation. Y'' - 6y' + 9y =

Solve the differential equation. Y'' - 6y' + 9y = 0

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Q: Use power series to solve the differential equation. y' =

Use power series to solve the differential equation. y' = x2y

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