Read the first two sections of Chapter 13 in the text as if they were
not going to be explained carefully in class.
The location at time t of a particle moving in space is
given by:
For each value of t find the following:
the acceleration.
the (i) parallel and (ii) perpendicular projections of acceleration
on velocity.
the (scalar) curvature.
the principal unit normal vector.
the equation of the osculating plane, which is the plane
through the point on the curve containing both the velocity and the
acceleration.
Do exercise 17 on p. 895: evaluate the double integral of the function
taken over the triangular region in the (x, y) plane with
vertices at (0, 0), (0, 1), and (1, 1).
Find the double integral of the function
f(x, y) = x^{2} y + x y^{3} over the planar region that is
bounded by the parabola y = 4 - x^{2} and the line
y = -3 x.
Reverse the order of iteration in the expression
|
INT[_{0}^{2} INT[_{0}^{e^{x}} dy ] dx ] .
|
What geometric quantity does this iterated integral represent?