Need help in determining the lim

  • Thread starter Thread starter Equilibrium
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit of a rational function as x approaches 4, specifically the expression \(\lim_{x\rightarrow 4}\frac{x^2 - 3x + 4}{2x^2 - x - 1}\). Participants are exploring whether factoring is necessary for this limit evaluation.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants suggest evaluating the limit directly by substituting x = 4, while others mention the possibility of factoring the expression. There is a discussion about the conditions under which factoring might be necessary.

Discussion Status

The discussion is active, with participants offering different perspectives on whether direct substitution is sufficient or if factoring is required. There is no explicit consensus on the best approach, but multiple interpretations are being explored.

Contextual Notes

Participants are considering the continuity of the function and the implications of substituting x = 4, particularly regarding potential undefined values in the denominator.

Equilibrium
Messages
81
Reaction score
0
Hi

[tex]\lim_{x\rightarrow 4}\frac{x^2 - 3x + 4}{2x^2 - x - 1}[/tex]

this is lim x ->4 which is the cube root of the whole fraction ^

Is there any way to answer this because i can't really factor it...
 
Last edited:
Physics news on Phys.org
Why not just evaluate the limit at [itex]x = 4[/itex]?
 
You don't need to factor it. It can easily be factored, since it's a ratio of quadratic polynomials.

Daniel.
 
Assuming f(x) is continuous at f(a) ([tex]\lim_{x \rightarrow a^{+}} f(x) = f(a) =\lim_{x \rightarrow a^{-}} f(x)[/tex]) you can always just plug in a. The only time you would need to factor is if f(x) is not continuous at a or if plugging in a would result in an undefined function (0 in denominator). So yea, as courtigrad said, just substitute x=4. :-)
 
Last edited:

Similar threads

  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
4
Views
2K
Replies
14
Views
3K
Replies
15
Views
2K