Questions from General Calculus

Q: Show that F is a conservative vector field. Then find a

Show that F is a conservative vector field. Then find a function f such that F = ∇f.

Q: (a). What happens to the spiral tube in Example 2

(a). What happens to the spiral tube in Example 2 (see Figure 5) if we replace cos u by sin u and sin u by cos u? (b). What happens if we replace cos u by cos 2u and sin u by sin 2u?

Q: Determine whether or not the given set is (a) open

Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. {(x, y) | 1 < |x | < 2}

Q: 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) = -y i

Q: Maxwell’s equations relating the electric field E and magnetic field H as

Maxwell’s equations relating the electric field E and magnetic field H as they vary with time in a region containing no charge and no current can be stated as follows: where c is t...

Q: Let S be the surface of the box enclosed by the planes

Let S be the surface of the box enclosed by the planes x = ±1, y = ±1, z = ±1. Approximate ∫∫S cos (x + 2y + 3z) dS by using a Riemann sum as in Definition 1, taking the patches Sij to be the squares...

Q: A surface S consists of the cylinder x2 + y2 = 1

A surface S consists of the cylinder x2 + y2 = 1, -1 Estimate the value of ∫∫S f (x, y, z) dS by using a Riemann sum, taking the patches Sij to be four quarter-...

Q: Identify the surface with the given vector equation. r (

Identify the surface with the given vector equation. r (s, t) = 〈s cos t, s sin t, s〉

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: 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.