A question on limits

  • Thread starter Manni
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  • #1
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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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  • #2
micromass
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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??
 
  • #3
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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?
 
  • #4
micromass
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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.
 
  • #5
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How do I show algebraically that Q approaches infinity as P approaches the origin?
 
  • #6
micromass
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How do I show algebraically that Q approaches infinity as P approaches the origin?

It doesn't approach infinity.

Did you find the expression for Q?
 

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