A question on limits

  1. I need help with this question. I understand that logic behind it; as P approaches O the value the right bisector Q reaches it's maximum. I don't know how to show this algebraically however. Help?
     

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  3. micromass

    micromass 18,426
    Staff Emeritus
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    We give P the coordinates (x,y). We know that P is on the parabola, so we know that

    [tex]P=(x,x^2)[/tex]

    Now, can you find the coordinates of the point Q??
     
  4. Ok, so the bisector would intersect P at point x/2. Because I know that the x coordinate on Q is 0, how would I find it's y?
     
  5. micromass

    micromass 18,426
    Staff Emeritus
    Science Advisor

    Answer the following steps:

    - Find the midpoint M between 0 en P.
    - Find the equation of the line L going through 0 and P
    - Find a vector perpendicular to the line L
    - Construct the equation of the line R going through M and perpendicular through L
    - Find Q as the intersection between R and the y-axis.

    All of these questions involve nothing more than 10th grade geometry. So you should be able to complete these easily.
     
  6. How do I show algebraically that Q approaches infinity as P approaches the origin?
     
  7. micromass

    micromass 18,426
    Staff Emeritus
    Science Advisor

    It doesn't approach infinity.

    Did you find the expression for Q?
     
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