Limits question ((x+1)/(x-1)-3)/(x-2)

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Homework Help Overview

The problem involves evaluating the limit of the expression \(\frac{(x+1)/(x-1)-3}{x-2}\) as \(x\) approaches a certain value, with a focus on understanding the behavior of the function around that point.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of algebraic manipulation and the use of l'Hôpital's rule. There are attempts to simplify the expression and check for errors in algebraic steps. Questions about the validity of the algebraic transformations are raised.

Discussion Status

The discussion is ongoing, with some participants providing guidance on checking algebraic work. There is a mix of confidence and uncertainty among participants regarding their understanding of the problem, and some express a shift towards seeking external help, such as a tutor.

Contextual Notes

Participants mention potential algebraic mistakes and the need for clarification on the steps taken in the solution process. There is also a discussion about the motivations behind seeking help from tutors versus peers.

venger
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Homework Statement


F(x) = [x+1 / x-1] coordinates (2,3)


Homework Equations


First principle Mtang=(F(x)-F(a))/x-a
second principle
finding the derivatives at first glance

The Attempt at a Solution


Mtang=(F(x)-F(a))/x-a
[x+1/x-1]-(3)/(x-2)
Multiply by (x-1/x-1) to get
x+1 - 3(x-1)
----------- <- over (fraction)
(x-2)(x-1)
<<
x+1-3
---------- <- Over (fraction)
(x-2)
<<
x-2
-----
x-2

equals ONE!
 
Last edited:
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Are you familiar with l'Hôpital's rule?
 
Last edited:
No I am not
 
Check your algebra going from the first 'over (fraction)' to the second one. You somehow made x-1 'disappear' through use of bad algebra. Simplify the numerator in the first expression.
 
Thats okay i know what to do know, 3x divided by x is 2x
 
venger said:
Thats okay i know what to do know, 3x divided by x is 2x

3x MINUS x is 2x. 3x divided by x is 3. Are you sure you know what to do?
 
well forget about it i got a tutor now
 
Good luck!
 
Meh, IMO, a tutor can only have a negative impact.
 
  • #10
How do we have a better impact than a tutor :S
 
  • #11
We don't but it doesn't exclude the fact that a tutor doesn't, IMO.
 
  • #12
Gib Z said:
How do we have a better impact than a tutor :S

Because we're doing it because we love mathematics and enjoy helping others. The tutor is doing it to make money, or because it's a required work-study job. :-p
 
  • #13
Lol Thats a good point, the only reason we would even be helping is because we want to, and because of that we put in our best effort. But id rather be half-assed AND get paid! :P
 

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