Questions from General Calculus

Q: Use the Divergence Theorem to calculate the surface integral ∫∫S F

Use the Divergence Theorem to calculate the surface integral ∫∫S F dS; that is, calculate the flux of F across S. S is the surface of the solid bounded by the...

Q: Use the Divergence Theorem to calculate the surface integral ∫∫S F

Use the Divergence Theorem to calculate the surface integral ∫∫S F dS; that is, calculate the flux of F across S. S is the surface of the solid bounded by the...

Q: Use the Divergence Theorem to calculate the surface integral ∫∫S F

Use the Divergence Theorem to calculate the surface integral ∫∫S F  dS; that is, calculate the flux of F across S. F = |r | r, where r = x i + y j + z k, S consists of the hemisphere z = √1 - x2 - y2...

Q: Use the Divergence Theorem to evaluate ∫∫S F ∙ dS

Use the Divergence Theorem to evaluate ∫∫S F ∙ dS, where F (x, y, z) = z2x i + (1/3 y3 + tan z) j + (x2z + y2) k and S is the top half of the sphere x2 + y2 + z2 = 1. [Hint: Note that S is not a clos...

Q: Evaluate the surface integral. ∫∫S (x + y

Evaluate the surface integral. ∫∫S (x + y + z) dS, S is the part of the half-cylinder x2 + z2 = 1, z > 0, that lies between the planes y = 0 and y = 2

Q: A vector field F is shown. Use the interpretation of divergence

A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P1 and at P2.

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) = x3yz2 j + y4z3 k

Q: Suppose S and C satisfy the hypotheses of Stokes’ Theorem and f

Suppose S and C satisfy the hypotheses of Stokes’ Theorem and f, t have continuous second-order partial derivatives. Use Exercises 24 and 26 in Section 16.5 to show the following. E...

Q: Verify that div E = 0 for the electric field E (

Verify that div E = 0 for the electric field E (x) = ∈Q |x |3 x.

Q: Use the Divergence Theorem to evaluate ∫∫S (2x + 2y

Use the Divergence Theorem to evaluate ∫∫S (2x + 2y + z2) dS where S is the sphere x2 + y2 + z2 = 1.