Chapter 10.3, Problem 92E

a)

To determine

Graph the curve by the use of graphing utility on the interval $-3\le t\le 3$

b)

To determine

$\frac{dy}{dx}$ and $\frac{d^{2}y}{d{x}^2}$

c)

To determine

The equation of tangent line at the point $\left(\sqrt{3},\frac{8}{3}\right)$

d)

To determine

Length of curve on the interval $-3\le t\le 3$.

e)

To determine

The area of surface generated by revolving the curve about $x-$ axis.