How Can We Rewrite the Limit and Continuity Equation Lim(x-->0) x/a[b/x]?

  • Context: Graduate 
  • Thread starter Thread starter Kartik.
  • Start date Start date
  • Tags Tags
    Continuity Limits
Click For Summary

Discussion Overview

The discussion revolves around the mathematical expression Lim(x-->0) x/a[b/x] and how it can be rewritten. Participants explore the implications of different notations and seek to clarify the transformation of the limit expression, focusing on continuity and limit behavior as x approaches 0.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that Lim(x-->0) x/a[b/x] can be expressed as x/a(b/x - {b/x}) and seeks further transformation.
  • Another participant questions the validity of the transformation, stating that the expression \lim_{x \to 0} \frac{a}{x} \frac{b}{x} does not equal \frac{x}{a} \left( \frac{b}{x} - \frac{b}{x} \right), indicating confusion over the notation used.
  • A participant clarifies that square brackets denote the greatest integer value and curly brackets represent the fractional part, which may influence the interpretation of the expressions.
  • Another participant reiterates the original transformation and points out that the term {b/x}/{b/x} simplifies to 1, suggesting a focus on the expression (b/x - b/a).

Areas of Agreement / Disagreement

Participants express differing views on the validity and meaning of the transformations proposed. There is no consensus on the correct interpretation or rewriting of the limit expression.

Contextual Notes

There are unresolved questions regarding the implications of the notations used, particularly the meanings of square and curly brackets, and how they affect the mathematical expressions being discussed.

Kartik.
Messages
55
Reaction score
1
Lim(x-->0) x/a[b/x] can be written as x/a(b/x-{b/x})

how can we write this as
lim(x-->0)
(b/x -b/a({b/x}/{b/x}))?
 
Physics news on Phys.org
Do [square] and {curly} brackets have some special meaning to you? Because
\lim_{x \to 0} \frac{a}{x} \frac{b}{x} \neq \frac{x}{a} \left( \frac{b}{x} - \frac{b}{x} \right)
doesn't really make sense to me.
 
CompuChip said:
Do [square] and {curly} brackets have some special meaning to you? Because
\lim_{x \to 0} \frac{a}{x} \frac{b}{x} \neq \frac{x}{a} \left( \frac{b}{x} - \frac{b}{x} \right)
doesn't really make sense to me.

Sorry, they are very common in my exercise books
square brackets mean the greatest integer value of the variable within and the curly brackets mean the fractional part of the variable within.
 
Kartik. said:
Lim(x-->0) x/a[b/x] can be written as x/a(b/x-{b/x})

how can we write this as
lim(x-->0)
(b/x -b/a({b/x}/{b/x}))?

Your question is a little confusing. You have a term {b/x}/{b/x} (=1??). So it seems you are asking about (b/x - b/a)?
 

Similar threads

MHB Is the Limit of Sin x/x=1 Proven in Elementary Calculus?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Definition of Limit for vector fields
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Some questions on l'Hôpital rules
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can we use removable discontinuities to extend a function to the entire plane?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
MHB 1.4.203 AP calculus practice question on Limits
  • · Replies 1 ·
Replies
1
Views
2K
High School Proof of Chain Rule: Understanding the Limits
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Analytic continuation of a dilogarithm
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why Does Factoring Change the Existence of a Limit in Spivak's Problem?
  • · Replies 6 ·
Replies
6
Views
2K