Questions from General Calculus


Q: Graph the two basic solutions along with several other solutions of the

Graph the two basic solutions along with several other solutions of the differential equation. What features do the solutions have in common?

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Q: A particle moves along line segments from the origin to the points

A particle moves along line segments from the origin to the points s1, 0, 0d, s1, 2, 1d, s0, 2, 1d, and back to the origin under the influence of the force field F (x, y, z) = z2 i + 2xy j + 4y2 k Fin...

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Q: The figure shows a pendulum with length L and the angle θ

The figure shows a pendulum with length L and the angle θ from the vertical to the pendulum. It can be shown that θ, as a function of time, satisfies the nonlinear differenti...

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Q: If S is a sphere and F satisfies the hypotheses of Stokes’

If S is a sphere and F satisfies the hypotheses of Stokes’ Theorem, show that ∫∫S curl F ∙ dS = 0.

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Q: (a). Are the points P1 and P2 sources or sinks

(a). Are the points P1 and P2 sources or sinks for the vector field F shown in the figure? Give an explanation based solely on the picture. (b). Given that F (x, y) = 〈x, y2â&#...

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Q: Solve the differential equation using (a) undetermined coefficients and (

Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.

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Q: Solve the differential equation using (a) undetermined coefficients and (

Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.

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Q: State Kepler’s Laws.

State Kepler’s Laws.

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Q: Find a parametric representation for the surface. The part of

Find a parametric representation for the surface. The part of the cylinder x2 + z2 = 9 that lies above the xy-plane and between the planes y = -4 and y = 4

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Q: Assume that the earth is a solid sphere of uniform density with

Assume that the earth is a solid sphere of uniform density with mass M and radius R = 3960 mi. For a particle of mass m within the earth at a distance r from the earth’s center, the gravitational forc...

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