Help with parametric equations for tangent line

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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.

Thanks in advance.
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

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