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Parametric Equations (Calc.2)

  1. Apr 1, 2013 #1
    1. The problem statement, all variables and given/known data

    Parametrize the curve by a pair of differentiable functions x = x(t), y = y(t) with [x '(t)]2 + [y '(t)]2≠0, then determine the tangent line at the origin.

    y=2x^3

    3. The attempt at a solution

    Honestly I don't really understand what it's asking for. I assume it wants us to make 2 equations, x= something and y = something but I'm not quite sure how to get there. Then we can find the tangent line by taking the derivative.

    Unfortunately I can't even show work on this problem since I don't even know where to start. Would appreciate any help on this question <3
     
  2. jcsd
  3. Apr 1, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    "Parametric equations" for a curve in the xy-plane are two equation x= f(t), y= g(t) such that, for any t, the corresponding point (x(t), y(t)) is a point on the curve. In particular, if the curve is given a function, y= F(x), we can just write x= t, y= F(t).
     
  4. Apr 1, 2013 #3
    Hmmmm right... So I'm a bit confused on how we take our starting equation and turn it into two.

    Would we just do

    y=2x^3 and x = (y/2)^1/3 ?
     
  5. Apr 1, 2013 #4
    Hmmmm right... So I'm a bit confused on how we take our starting equation and turn it into two.

    Would we just do

    y=2t^3 and x = (t/2)^1/3 ?
     
  6. Apr 1, 2013 #5

    Mark44

    Staff: Mentor

    No. Here you are apparently finding the inverse of the function. The first equation has y as a function of x, and the second has x as a function of y.

    Your first equation can be symbolized as y = f(x), and the second as x = f-1(y).
    That's not what you need to do.

    No. How about x = t? What would y be then, as a function of t?
     
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