# Help with parametric equations for tangent line

• November 16th 2008, 12:10 PM
khuezy
Help with parametric equations for tangent line
Consider the curve r (t) = < t + 2t^3, t + e^t >
Find parametric equations for the tangent line at (0, 1)

This occurs at t=0
dydt/dxdt = (1+e^0) / (1+6(0)^2) = 2/1 = 2

Am I doing this right?

(b) Find all t such that the tangent line is vertical.

• November 16th 2008, 02:43 PM
khuezy
?
anyone?
• November 16th 2008, 02:54 PM
Plato
Part a
$\begin{gathered}
r(t) = \left\langle {t + 2t^3 ,t + e^t } \right\rangle \Rightarrow \quad r'(t) = \left\langle {1 + 6t,1 + e^t } \right\rangle \hfill \\
r'(0) = \left\langle {1,2} \right\rangle \hfill \\
l = \left\{ \begin{gathered}
x = t \hfill \\
y = 2t + 1 \hfill \\
\end{gathered} \right. \hfill \\
\end{gathered}$
• November 16th 2008, 05:31 PM
khuezy
thx
is part b.) t=0?
• November 17th 2008, 02:35 AM
HallsofIvy
No. a "vertical" vector must be of the form < 0, y>. When is the x component of the r' vector 0?
• November 17th 2008, 07:33 AM
khuezy
k
-1/6
thanks