Given

r$($t$)=$

$8$et$,$ et cos$($t$),$ et sin$($t$)$

$,$

determine each of the following.

$($a$)$

the unit tangent vector

T$($t$)$

T$($t$)=$

$($b$)$

the unit tangent vector

T$($t$)$

evaluated at

t $=0$

T$(0)=$

$($c$)$

the unit normal vector

N$($t$)$

evaluated at

t $=0$

$($d$)$

the unit binormal vector

B$($t$)$

evaluated at

t $=0$