Questions from General Calculus

Q: Use Green’s Theorem in the form of Equation 13 to prove Green’s

Use Green’s Theorem in the form of Equation 13 to prove Green’s first identity: where D and C satisfy the hypotheses of Green’s Theorem and the...

Q: Find an equation of the tangent plane to the given parametric surface

Find an equation of the tangent plane to the given parametric surface at the specified point.

Q: Find an equation of the tangent plane to the given parametric surface

Find an equation of the tangent plane to the given parametric surface at the specified point.

Q: Find an equation of the tangent plane to the given parametric surface

Find an equation of the tangent plane to the given parametric surface at the specified point.

Q: Evaluate the line integral. ∫C F ∙ dr,

Evaluate the line integral. ∫C F ∙ dr, where F (x, y, z) = ez i + xz j + (x + y) k and C is given by r (t) = t2 i + t3 j - t k, 0 < t < 1

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

Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies in the first octant

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) = sin yz i + sin zx j + sin xy k

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

Find the area of the surface. The part of the plane with vector equation

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

Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 3

Q: Find the area of the surface. The surface z =

Find the area of the surface. The surface z = 2/3 (x3/2 + y3/2), 0 < x < 1, 0 < y < 1