Questions from General Calculus

Q: Let f be a scalar field and F a vector field.

Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar field or a vector field. (a). curl f (b). grad f (c...

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∆f. F (x, y, z) = y2z3 i + 2xyz3 j + 3xy2z2 k

Q: (a). Define the gradient vector ∇f for a function

(a). Define the gradient vector ∇f for a function f of two or three variables. (b). Express Du f in terms of ∇f. (c). Explain the geometric significance of the gradient.

Q: Verify Green’s Theorem by using a computer algebra system to evaluate both

Verify Green’s Theorem by using a computer algebra system to evaluate both the line integral and the double integral. P (x, y) = x3y4, Q (x, y) = x5y4, C consists of the line segment from (-π/2, 0) t...

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = i + sin z j + y cos z k

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = eyz i + xzeyz j + xyeyz k