Multi-Variable Calculus Assignment

due Friday, March 30, 2001

Reading Assignment

Read the first two sections of Chapter 13 in the text as if they were not going to be explained carefully in class.

Exercises

1. The location at time t of a particle moving in space is given by:

x = 4 cos t
y = 4 sin t
z = 3t

For each value of t find the following:

(a) the acceleration.

(b) the (i) parallel and (ii) perpendicular projections of acceleration on velocity.

(c) the (scalar) curvature.

(d) the principal unit normal vector.

(e) the equation of the osculating plane, which is the plane through the point on the curve

containing both the velocity and the acceleration.

2. Do exercise 17 on p. 895: evaluate the double integral of the function

f(x, y) = x + y

taken over the triangular region in the (x, y) plane with vertices at (0, 0), (0, 1), and (1, 1).

3. Find the double integral of the function f(x, y) = x^{2}y + xy^{3} over the planar region that is bounded by the parabola y = 4 − x^{2} and the line y = −3x.

4. Reverse the order of iteration in the expression

∫_{0}^{2} ∫_{0}^{e^{x}} dydx .

What geometric quantity does this iterated integral represent?