Limits: Finding the Value of (x - Sinx) / x^3

  • Thread starter Thread starter rambo5330
  • Start date Start date
  • Tags Tags
    Limits Value
Click For Summary

Homework Help Overview

The problem involves evaluating the limit as x approaches 0 of the expression (x - Sinx) / x^3, which falls under the subject area of calculus, specifically limits and series expansions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss potential methods for evaluating the limit, including L'Hôpital's Rule and the Maclaurin series expansion for sin x. There is uncertainty about the application of these techniques, particularly for those unfamiliar with them.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the limit. Some guidance has been provided regarding L'Hôpital's Rule and series expansion, but there is no consensus on a preferred method yet.

Contextual Notes

One participant expresses a lack of familiarity with L'Hôpital's Rule and series expansions, indicating a potential gap in prerequisite knowledge for the techniques being discussed.

rambo5330
Messages
83
Reaction score
0

Homework Statement


lim (x->0) of (x - Sinx) / x^3


Homework Equations





The Attempt at a Solution


I would like to know the proper route for analyzing that question... the text is saying i should end up with 1/6 ...however I'm not sure how they arrived at that answer ...
 
Physics news on Phys.org
Are you familiar with l'hopitale's rule?

if lim (x->0) a/b = 0/0 or infinity/infitity then lim (x->0) a/b = lim (x->0) a'/b'
 
not familiar with that yet ...
 
Another approach is to replace sin x by a few terms of its Maclaurin series, but if you don't know L'Hopital's Rule, you probably don't know anything about series yet, either. Short of those two techniques, I can't think of anything else that would work for you.
 

Similar threads

  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
24
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
8
Views
2K