Lim x to 0 (1/sinx - 1/x ) is equals to infinity?

  • Thread starter Thread starter teng125
  • Start date Start date
  • Tags Tags
    Infinity
Click For Summary

Homework Help Overview

The discussion revolves around the limit of the expression (1/sin(x) - 1/x) as x approaches 0, specifically questioning whether it equals infinity. The subject area is calculus, focusing on limits and indeterminate forms.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to rewrite the expression to identify an indeterminate form suitable for applying L'Hospital's Rule. There are questions about the conditions under which L'Hospital's Rule can be applied.

Discussion Status

Some participants have provided guidance on rewriting the expression to achieve the necessary form for L'Hospital's Rule. There is an ongoing exploration of the conditions for applying this rule, but no consensus has been reached regarding the limit itself.

Contextual Notes

There is an emphasis on the requirement for the expression to be in the form of 0/0 or ∞/∞ to apply L'Hospital's Rule, indicating a focus on understanding the conditions for limit evaluation.

teng125
Messages
416
Reaction score
0
may i know is it lim x to 0 (1/sinx - 1/x ) is equals to infinity??
 
Physics news on Phys.org
You cannot apply L'Hospital on this function (yet), you'd need to rewrite it so that you get something of the form 0/0 or ∞/∞.
 
To apply L'Hospital's Rule, put the expression in theform f(x)/g(x). If the form is indeterminate, then you can apply the Rule.
 
daveb said:
To apply L'Hospital's Rule, put the expression in theform f(x)/g(x). If the form is indeterminate, then you can apply the Rule.
Just to avoid confusion: it has to be 0/0 or ∞/∞ as I said, since there are more indeterminate forms possible. Many can be reduced to one of the two 'allowed' ones to use the rule though.
 
okok.thanx
 

Similar threads

Limit of 0^0: Evaluating x^sinx
  • · Replies 19 ·
Replies
19
Views
2K
Finding the limit using a trig identity
  • · Replies 5 ·
Replies
5
Views
2K
Calculation of limit. L'Hopital's rule
  • · Replies 3 ·
Replies
3
Views
2K
How Does Substitution Affect Double Integration and Differentiation?
  • · Replies 3 ·
Replies
3
Views
2K
Problem 1-23 and 1-24 from Spivak's Calculus on Manifolds
  • · Replies 6 ·
Replies
6
Views
2K
Finding the Maximum Value of f(x)=x(1-x)^n in [0,1]: A Calculus Problem
  • · Replies 3 ·
Replies
3
Views
2K
Integrating (sin(x))/x dx -- The limits are a=0 and b=infinitity
  • · Replies 3 ·
Replies
3
Views
2K
On the ratio test for power series
  • · Replies 2 ·
Replies
2
Views
2K
Optimization Problem: x_1(sin(x_1)) such that exp(x_1)-1>=0
  • · Replies 2 ·
Replies
2
Views
1K
Calculating Limits Using Properties
  • · Replies 4 ·
Replies
4
Views
2K