$(2$ points$)$

Find the limit:

$(2$ points$)$ Find a parametrization of the circle of radius $4$ in the $xy-$plane, centered at the origin, oriented clockwise. The point $(4,0)$ should correspond to $t=0.$ Use $t$ as the parameter for all of your answers.

$x(t)=$

$y(t)$

$(2$ points$)$ Find a vector parametric equation vec$(r)(t)$ for the line through the points $P=(-2,5,3)$ and $Q=(-6,6,-2)$ for each of the given conditions on the parameter $t$

$($a$)$ If vec$(r)(0)=($:$-2,5,3$:$)$ and vec$(r)(3)=($:$-6,6,-2$:$).$ then

vec$(r)(t)=$

$($b$)$ If vec$(r)(6)=P$ and vec$(r)(8)=Q,$ then

vec$(r)(t)=$

$($c$)$ If the points $P$ and $Q$ correspond to the parameter values $t=0$ and $t=-2,$ respectively, then

vec$(r)(t)=$