Another limit using l'hopitals

  • Thread starter Thread starter magnifik
  • Start date Start date
  • Tags Tags
    Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit as x approaches infinity of the expression (1/x^2) - (cscx)^2. Participants are exploring the conditions under which this limit can be classified as indeterminate.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to determine how to express the limit in an indeterminate form. There is a suggestion to rewrite csc(x)^2 in terms of sin(x) to facilitate the analysis. Questions are raised regarding the limiting behavior of the individual components of the expression as x approaches infinity.

Discussion Status

The discussion is ongoing, with participants clarifying the original problem statement and questioning the indeterminate nature of the limit. Some guidance has been offered regarding rewriting the expression, but there is no consensus on the approach or outcome yet.

Contextual Notes

Participants are working under the assumption that the limit as x approaches infinity is correctly stated, despite some confusion about the conditions for indeterminate forms. There is mention of the need for a proof regarding the non-existence of the limit.

magnifik
Messages
350
Reaction score
0

Homework Statement


limit as x goes to infinity of (1/x^2) - (cscx)^2


Homework Equations





The Attempt at a Solution


I made it so the denominator is x^2, but then it would 1-inf/inf which isn't indeterminate. i need help setting it up so it would be in indeterminate form. thanks.
 
Physics news on Phys.org
You probably mean lim x->0, right? Just make a common denominator and combine those two terms into a single fraction. It's probably easier to write 1/sin(x)^2 instead of csc(x)^2, but it will still take several derivatives before you get a nonindeterminant answer from l'Hopital.
 
Last edited:
nope, the question states lim x-> inf
 
magnifik said:
nope, the question states lim x-> inf

Then tell me about the limiting behavior of 1/x^2 and csc(x)^2 as x->inf. Is that expression really indeterminant?
 
that's what my original problem was
 
magnifik said:
that's what my original problem was

Sketch a graph of each one. The limiting behavior should be visually obvious.
 
magnifik said:

Homework Statement


limit as x goes to infinity of (1/x^2) - (cscx)^2


Homework Equations





The Attempt at a Solution


I made it so the denominator is x^2, but then it would 1-inf/inf which isn't indeterminate. i need help setting it up so it would be in indeterminate form. thanks.

The limit does not exist by any means. If needed, a proof can be given.

AB
 

Similar threads

How to solve a limit in two variables with an indeterminate form at (0,0)?
  • · Replies 35 ·
2
Replies
35
Views
5K
Limit of a_n as n Approaches Infinity & Zero
  • · Replies 24 ·
Replies
24
Views
2K
Verify a limit using L'Hopital's Rule
  • · Replies 14 ·
Replies
14
Views
2K
Stuck on Applying L'Hopital's Rule to Indeterminant Form
  • · Replies 2 ·
Replies
2
Views
2K
Calculation of limit. L'Hopital's rule
  • · Replies 3 ·
Replies
3
Views
2K
Finding limits with a radical in denominator
  • · Replies 5 ·
Replies
5
Views
2K
Limit - Squeeze Theorem or L'Hopital's Rule?
  • · Replies 3 ·
Replies
3
Views
7K
What is my mistake in solving for this limit?
  • · Replies 23 ·
Replies
23
Views
2K
Need help finding the limit of a function
  • · Replies 5 ·
Replies
5
Views
2K
Limit of (-x^(k+1))/e^x: Solving Step by Step with l'Hopital's Rule
  • · Replies 5 ·
Replies
5
Views
2K