Questions from General Calculus

Q: (a). How do you find the velocity, speed,

(a). How do you find the velocity, speed, and acceleration of a particle that moves along a space curve? (b). Write the acceleration in terms of its tangential and normal components.

Q: Match the vector fields F with the plots labeled I–IV

Match the vector fields F with the plots labeled I–IV. Give reasons for your choices. F (x, y) = 〈x, -y〉

Q: Is the vector field shown in the figure conservative? Explain.

Is the vector field shown in the figure conservative? Explain.

Q: Use the method of Example 5 to calculate ∫C F ∙

Use the method of Example 5 to calculate ∫C F ∙ dr, where and C is any positively oriented simple closed curve that encloses the origin.

Q: Let F = ∇f, where f (x, y

Let F = ∇f, where f (x, y) = sin (x - 2y). Find curves C1 and C2 that are not closed and satisfy the equation.

Q: Use Green’s Theorem to prove the change of variables formula for a

Use Green’s Theorem to prove the change of variables formula for a double integral (Formula 15.9.9) for the case where f (x, y) = 1: Here R is the region in the xy-plane that corre...

Q: Determine whether or not the given set is (a) open

Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected. {(x, y) | 1 < x2 + y2 < 4, y > 0}

Q: (a). Evaluate the line integral ∫C F ∙

(a). Evaluate the line integral ∫C F ∙ dr, where F (x, y) = ex-1 i + xy j and C is given by r(t) = t2 i + t3 j, 0 (b). Illustrate part (a) by using a graphing calc...

Q: (a). Find the work done by the force field F

(a). Find the work done by the force field F (x, y) = x2 i + xy j on a particle that moves once around the circle x2 + y2 = 4 oriented in the counterclockwise direction. (b). Use a computer algebra sy...

Q: (a). What is a parametric surface? What are its

(a). What is a parametric surface? What are its grid curves? (b). Write an expression for the area of a parametric surface. (c). What is the area of a surface given by an equation z = t (x, y)?