Q: (a). What does it mean to say that ∫C
(a). What does it mean to say that ∫C F ∙ dr is independent of path? (b). If you know that ∫C F ∙ dr is independent of path, what can you say about F?
See AnswerQ: Consider the boundary-value problem y'' - 2y' + 2y =
Consider the boundary-value problem y'' - 2y' + 2y = 0, y (a) = c, y (b) = d. (a). If this problem has a unique solution, how are a and b related? (b). If this problem has no solution, how are a, b, c...
See AnswerQ: (a). Suppose that F is an inverse square force field
(a). Suppose that F is an inverse square force field, that is, F (r) = cr/ |r |3 for some constant c, where r = x i + y j + z k. Find the work done by F in moving an object from a point P1 along a pat...
See AnswerQ: Find a formula for ∫∫S F dS similar to Formula
Find a formula for ∫∫S F dS similar to Formula 10 for the case where S is given by y = h (x, z) and n is the unit normal that points toward the left.
See AnswerQ: Find a formula for ∫∫S F dS similar to Formula
Find a formula for ∫∫S F dS similar to Formula 10 for the case where S is given by x = k (y, z) and n is the unit normal that points forward (that is, toward the viewer when the axes are drawn in th...
See AnswerQ: How do you find a tangent plane to each of the following
How do you find a tangent plane to each of the following types of surfaces? (a). A graph of a function of two variables, z = f (x, y) (b). A level surface of a function of three variables, F (x, y, z)...
See AnswerQ: (a). What does it mean to say that f is
(a). What does it mean to say that f is differentiable at (a, b)? (b). How do you usually verify that f is differentiable?
See AnswerQ: Sketch the vector field F by drawing a diagram like Figure 5
Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9. Figure 9: F (x, y, z) = z i
See AnswerQ: Let S be the part of the sphere x2 + y2 +
Let S be the part of the sphere x2 + y2 + z2 = 25 that lies above the plane z = 4. If S has constant density k, find (a) the center of mass and (b) the moment of inertia about the z-axis.
See AnswerQ: The figure shows a vector field F and two curves C1 and
The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1 and C2 positive, negative, or zero? Explain.
See Answer
