Need Help Understanding Limits Question Algebraically

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In summary, the conversation discusses finding the coordinates of point Q on a parabola as P approaches the origin. The steps involve finding the midpoint between 0 and P, the equation of the line passing through 0 and P, a vector perpendicular to that line, and the equation of the line passing through the midpoint and perpendicular to the first line. The process does not involve advanced math and can be easily solved with 10th grade geometry. It is also noted that Q does not approach infinity as P approaches the origin.
  • #1
Manni
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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
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
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
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
How do I show algebraically that Q approaches infinity as P approaches the origin?
 
  • #6
Manni said:
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?
 

Related to Need Help Understanding Limits Question Algebraically

1. What is a limit in algebra?

A limit in algebra refers to the value that a function approaches as the input value gets closer and closer to a specified point. It is used to describe the behavior of a function near a certain point, and is written in the form of "lim x→a f(x)".

2. How do you find a limit algebraically?

To find a limit algebraically, you can use various methods such as direct substitution, factoring, and rationalizing the numerator or denominator. You can also use the limit laws to simplify the function and evaluate the limit.

3. What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only considers the behavior of a function as the input approaches the specified point from one side, either the left or the right. A two-sided limit considers the behavior of the function from both sides of the specified point.

4. What is the importance of understanding limits in algebra?

Understanding limits in algebra is crucial for understanding the behavior of functions and their graphs. It helps us determine the end behavior of a function, identify any discontinuities, and find important points such as vertical asymptotes and intercepts.

5. Are there any limitations to using algebra to understand limits?

While algebra can be a powerful tool for understanding limits, it may not always provide an accurate answer. In some cases, the limit may not exist or may require more advanced techniques such as L'Hôpital's rule. Additionally, algebra may not be able to fully capture the behavior of more complex functions.

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