Chapter 14.1, Problem 37E

a.

To determine

Whether the statement “The projection of curve line $r\left(t\right)=\langle t,\cos t,t^2\rangle$ in the xz-plane is parabola.” is true or not.

(b)

To determine

Whether the statement “The curve $r\left(t\right)=\langle \sin t,\cos t,\sin t\rangle$ lies on a unit circle.” is true or not.

(c)

To determine

Whether the statement “The curve $r\left(t\right)=\langle e^{-t},\sin t,-\cos t\rangle$ approaches a circle as $t\to \infty$.” is true or not.

(d)

To determine

Whether the statement “If $r\left(t\right)=e^{-t^2}\langle 1,1,1\rangle \text{, then }\underset{t\to \infty }{\lim }r\left(t\right)=\underset{t\to -\infty }{\lim }r\left(t\right)$.” is true or not.