Questions from General Calculus

Q: (a). What is a function of two variables?

(a). What is a function of two variables? (b). Describe three methods for visualizing a function of two variables.

Q: Match the vector fields F on R3 with the plots labeled I

Match the vector fields F on R3 with the plots labeled I–IV. Give reasons for your choices. F (x, y, z) = x i + y j + z k

Q: Plot the gradient vector field of f together with a contour map

Plot the gradient vector field of f together with a contour map of f. Explain how they are related to each other. f (x, y) = cos x - 2 sin y

Q: Match the functions f with the plots of their gradient vector fields

Match the functions f with the plots of their gradient vector fields labeled I–IV. Give reasons for your choices. f (x, y) = (x + y)2

Q: If you have a CAS that plots vector fields (the command

If you have a CAS that plots vector fields (the command is field plot in Maple and Plot Vector Field or Vector Plot in Mathematica), use it to plot F (x, y) = (y2 - 2xy) i +) (3xy - 6x2) j Explain the...

Q: A particle moves in a velocity field V (x, y

A particle moves in a velocity field V (x, y) = 〈x^2, x, + y^2 〉 If it is at position s2, 1d at time t − 3, estimate its location at time t = 3.01.

Q: Determine whether the points P and Q lie on the given surface

Determine whether the points P and Q lie on the given surface. r (u, v) = 〈u + v, u - 2v, 3 + u – v〉 P (4, -5, 1), Q (0, 4, 6)

Q: Determine whether the points P and Q lie on the given surface

Determine whether the points P and Q lie on the given surface. r (u, v) = 〈1 + u - v, u + v2, u2 - v2〉 P (1, 2, 1), Q (2, 3, 3)

Q: Identify the surface with the given vector equation. r (

Identify the surface with the given vector equation. r (u, v) = (u + v) i + (3 – v) j + (1 + 4u + 5v) k

Q: Show that the line integral is independent of path and evaluate the

Show that the line integral is independent of path and evaluate the integral. ∫C sin y dx + (x cos y - sin y) dy, C is any path from (2, 0) to (1, π)