Chapter 13.1, Problem 12E

To determine

Show that the path given by $r(t)=\langle e^{-t}\sin t,e^{-t}\cos t,e^{-t}\rangle$ intersects the sphere $x^2+y^2+z^2=4$ once, travelling from outside the sphere to inside as t goes form $-\infty \text{to}\infty .$