Multivariable Calculus

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Moderate

Tangent Line to Curve at Point

MVCALC-N3JVLE

What is a correct set of parametric equations for the tangent line to the curve:

$${\bf r}(t)=\cos t{\bf i} + \sin t {\bf j} +2t{\bf k}$$

...at the point $P=(-1,0,2\pi)$?

A

$x=-1$, $y=-2s$, $z=2\pi+2s$

B

There is no tangent line to the curve at $P$, since $P$ is not smooth at that point.

C

$x=1$, $y=-s$, $z=2\pi+s$

D

There is no tangent line to the curve at $P$, since $P$ is not on the curve.

E

$x=-1$, $y=-s$, $z=2\pi+2s$