Can Random Methods and Limits Improve My Understanding of Numbers?

  • Context: High School 
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Discussion Overview

The discussion revolves around understanding limits in calculus, specifically through a test problem involving the limit of a function as it approaches a certain value. Participants explore different methods for solving the problem and express their learning experiences in calculus.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant requests a simple test problem involving limits and suggests using random methods (Substitution, Factorization, Conjugation).
  • Another participant presents the limit problem lim_{x\rightarrow 4}\frac {2x-8}{\sqrt x - 2} and expresses uncertainty about their solution.
  • A participant challenges the correctness of the solution provided, suggesting that the participant should simplify 0/2 and hints at rationalizing the denominator as a potential method.
  • There is a request for step-by-step guidance on solving the limit problem, indicating a desire for a clearer understanding of the process involved.
  • A participant shares a personal anecdote about struggling with similar problems and appreciates the concept of limits, providing a metaphorical example involving a train's arrival time to illustrate the idea of approaching a limit.

Areas of Agreement / Disagreement

Participants express differing levels of understanding and approaches to solving the limit problem. There is no consensus on the correct method or solution, and the discussion remains unresolved regarding the best approach to the problem.

Contextual Notes

Participants mention various methods for solving limits but do not agree on the effectiveness or applicability of these methods in the given context. There are indications of missing steps in the problem-solving process, and some participants express confusion about certain mathematical concepts.

Who May Find This Useful

This discussion may be useful for individuals learning calculus, particularly those seeking to understand limits and different methods for solving limit problems.

Oh the irony
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Can someone give me a little test problem? An easy one please, I'm new to this lol.
Make the method random, so I have to try all three. Sub,Fac,Conj
 
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Oh the irony said:
Can someone give me a little test problem? An easy one please, I'm new to this lol.
Make the method random, so I have to try all three. Sub,Fac,Conj

[tex]lim_{x\rightarrow 4}\frac {2x-8}{\sqrt x - 2}[/tex]
 


LCKurtz said:
[tex]lim_{x\rightarrow 4}\frac {2x-8}{\sqrt x - 2}[/tex]
Uhh, I doubt I got it right lol butttt0/2?

If I didn't get it right, can you show me how to do it please? I'm trying to learn calculus by myself... lol I know. I just really want to learn it.
 


No, that isn't right. And even though it's wrong, you would normally simplify 0/2 wouldn't you?

I'll give you a hint. Try rationalizing the denominator.
 


LCKurtz said:
No, that isn't right. And even though it's wrong, you would normally simplify 0/2 wouldn't you?

I'll give you a hint. Try rationalizing the denominator.

lol, Like I said.. Can you show me how to do it.

I seriously just kinda started learning this stuff by myself. I can grasp it, if someone can show me the steps. If I can see the steps, I can understand it. Unless there are certain rules of course that go along with it but those are technically steps.

I don't see how I can rationalize it.
 


Haha, that kind of problem haunted me for a long time.

It is specifically because of those problems I appreciate the beauty of the number 1 and the amazing cleverness of it. It also illuminated all that complex multiplication I memorized without a thought to the why :biggrin:

Anyway, www.khanacademy.org has some amazing videos on limits, you should watch them all to get a grasp of what you're doing.

I'll quote something from my book that I think was just a great real life description of limits;

Let us imagine a traveller on a train due in New York at 5:17pm.
He must be there on time, so he continually looks at his watch and checks with the timetable.
He notices:
5.01pm the train is 10 miles out.
5:10pm, the train is 1 mile out.
5:17 exactly the train pulls up at its platform in Grand Central Terminal.

As the distance between the train station and the passenger approaches zero, the time reaches the maximum time allowed: 5:17
 

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