Questions from General Calculus

Q: A hemisphere H and a portion P of a paraboloid are shown

A hemisphere H and a portion P of a paraboloid are shown. Suppose F is a vector field on R3 whose components have continuous partial derivatives. Explain why

Q: Solve the differential equation or initial-value problem using the method

Solve the differential equation or initial-value problem using the method of undetermined coefficients.

Q: Verify that the Divergence Theorem is true for the vector field F

Verify that the Divergence Theorem is true for the vector field F on the region E. F (x, y, z) = 〈z, y, x〉, E is the solid ball x2 + y2 + z2 < 16

Q: Solve the differential equation or initial-value problem using the method

Solve the differential equation or initial-value problem using the method of undetermined coefficients.

Q: (a). What is an oriented surface? Give an example

(a). What is an oriented surface? Give an example of a non-orientable surface. (b). Define the surface integral (or flux) of a vector field F over an oriented surface S with unit normal vector n. (c)....

Q: Use a computer to graph the parametric surface. Get a printout

Use a computer to graph the parametric surface. Get a printout and indicate on it which grid curves have u constant and which have v constant.

Q: Solve the differential equation or initial-value problem using the method

Solve the differential equation or initial-value problem using the method of undetermined coefficients.

Q: Use Stokes’ Theorem to evaluate ∫C F ∙ dr.

Use Stokes’ Theorem to evaluate ∫C F ∙ dr. In each case C is oriented counterclockwise as viewed from above. F (x, y, z) = 2y i + xz j + (x + y) k, C is the curve of intersection of the plane z = y +...

Q: Graph the particular solution and several other solutions. What characteristics do

Graph the particular solution and several other solutions. What characteristics do these solutions have in common? y'' + 3y' + 2y = cos x

Q: Let F (x, y, z) = z tan

Let F (x, y, z) = z tan-1 (y2) i + z3 ln (x2 + 1) j + z k. Find the flux of F across the part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward.