Questions from General Calculus


Q: (a) Find a function f such that F = ∇

(a) Find a function f such that F = ∇f and (b) use part (a) to evaluate ∫C F ∙ dr along the given curve C. 12.

See Answer

Q: (a) Find a function f such that F = ∇

(a) Find a function f such that F = ∇f and (b) use part (a) to evaluate ∫C F ∙ dr along the given curve C. 12.

See Answer

Q: (a) Find a function f such that F = ∇

(a) Find a function f such that F = ∇f and (b) use part (a) to evaluate ∫C F ∙ dr along the given curve C. 12.

See Answer

Q: Use Green’s Theorem to evaluate ∫C x2y dx - xy2 dy

Use Green’s Theorem to evaluate ∫C x2y dx - xy2 dy, where C is the circle x2 + y2 = 4 with counterclockwise orientation.

See Answer

Q: A table of values of a function f with continuous gradient is

A table of values of a function f with continuous gradient is given. Find ∫C ∇f  dr, where C has parametric equations x = t2 + 1 y = t3 + t 0 < t < 1

See Answer

Q: If u and v are differentiable vector functions, c is a

If u and v are differentiable vector functions, c is a scalar, and f is a real-valued function, write the rules for differentiating the following vector functions. (a). u (t) + v (t) (b). cu (t) (c)...

See Answer

Q: Suppose an experiment determines that the amount of work required for a

Suppose an experiment determines that the amount of work required for a force field F to move a particle from the point (1, 2) to the point (5, -3) along a curve C1 is 1.2 J and the work done by F in...

See Answer

Q: Find the work done by the force field F in moving an

Find the work done by the force field F in moving an object from P to Q. F (x, y) = x3 i + y3 j; P (1, 0), Q (2, 2)

See Answer

Q: Find the work done by the force field F in moving an

Find the work done by the force field F in moving an object from P to Q. F (x, y) = (2x + y) i + x j; P (1, 1), Q (4, 3)

See Answer

Q: Find the gradient vector field ∆f of f and sketch it

Find the gradient vector field ∆f of f and sketch it. f (x, y) = ½ (x – y)2

See Answer