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Math Help - Help with parametric equations for tangent line

  1. #1
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    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.
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  2. #2
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    ?

    anyone?
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  3. #3
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    Part a
    \begin{gathered}<br />
  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 \\<br />
  r'(0) = \left\langle {1,2} \right\rangle  \hfill \\<br />
  l = \left\{ \begin{gathered}<br />
  x = t \hfill \\<br />
  y = 2t + 1 \hfill \\ <br />
\end{gathered}  \right. \hfill \\ <br />
\end{gathered}
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  4. #4
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    thx

    is part b.) t=0?
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  5. #5
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    No. a "vertical" vector must be of the form < 0, y>. When is the x component of the r' vector 0?
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  6. #6
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    k

    -1/6
    thanks
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