Questions from General Calculus

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the surface z = 4 - 2x2 + y that lies above the triangle with vertices (0, 0), (1, 0), and (1, 1)

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 1

Q: Suppose there is a hole in the can of paint in Exercise

Suppose there is a hole in the can of paint in Exercise 45 and 9 lb of paint leaks steadily out of the can during the man’s ascent. How much work is done? Exercise 45: A 160-lb man carries a 25-lb c...

Q: (a). Show that a constant force field does zero work

(a). Show that a constant force field does zero work on a particle that moves once uniformly around the circle x2 + y2 = 1. (b). Is this also true for a force field F (x) = kx, where k is a constant a...

Q: Find the area of the surface. The helicoid (or

Find the area of the surface. The helicoid (or spiral ramp) with vector equation

Q: If F = P i + Q j, how do you

If F = P i + Q j, how do you determine whether F is conservative? What if F is a vector field on R3?

Q: Find the area of the surface. The surface with parametric

Find the area of the surface. The surface with parametric equations x = u2, y = uv,

Q: Find (a) the curl and (b) the divergence

Find (a) the curl and (b) the divergence of the vector field. F (x, y, z) = √x/ 1 + z i + √y 1 + x j + √z 1 + y k

Q: Find (a) the curl and (b) the divergence

Find (a) the curl and (b) the divergence of the vector field. F (x, y, z) = ln (2y + 3z) i + ln (x + 3z) j + ln (x + 2y) k

Q: Find (a) the curl and (b) the divergence

Find (a) the curl and (b) the divergence of the vector field. F (x, y, z) = 〈ex sin y, ey sin z, ez sin x〉