Consider the path x(t) = (e−t cos t, e−t sin t). (a) Argue that the path spirals toward...

Consider the path x(t) = (e^−t cos t, e^−t sin t).

(a) Argue that the path spirals toward the origin as

(b) Show that, for any a, the improper integral converges.

(c) Interpret what the result in part (b) says about the path x.