Solve Homework: lim as x-1+ of 2^1/x-1=infinity

  • Thread starter Thread starter Bigo75
  • Start date Start date
  • Tags Tags
    Limits
Click For Summary

Homework Help Overview

The discussion revolves around evaluating limits, specifically focusing on the limit as x approaches 1 from the right for the expression 2^(1/x) - 1, which is suggested to approach infinity. Other limits are also mentioned, including those as x approaches 0 and 1 for different functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the evaluation of limits, with one participant expressing uncertainty about how to approach the limit from the right side. Others discuss bounding techniques related to sine functions in a different limit context.

Discussion Status

Some participants provide insights into bounding functions and suggest methods for approaching limits, while others express difficulty with specific problems. There is no explicit consensus on the limit in question, but there are productive discussions about related concepts.

Contextual Notes

One participant notes a lack of clarity in evaluating limits from the right-hand side, indicating potential gaps in understanding or information. The original poster also mentions using delta-epsilon proofs, suggesting a formal approach to limit evaluation.

Bigo75
Messages
8
Reaction score
0

Homework Statement


A) lim as x-1 of x^2-x+1/x+1 =1/2

B)lim as x-0 of x^2 sin(1/x)=0

C) lim as x-1+ of 2^1/x-1=infinity

Homework Equations


By delta-epsilon proofs


The Attempt at a Solution



A) I took |f(x)-l| and could not factor out an x-1

B) I know that x^2 goes to 0 and that the compositions of functions have the same limit.

C) I have no clue how to evaluate limits from the right hand side!
 
Physics news on Phys.org
for B, |x^2sin(1/x)| = |x^2||sin(1/x)| <= ...


what do you know about the sine function? for all u we have |sin(u)| <= ...?
 
that it is bounded by 1
 
right, so let e > 0, and choose d = sqrt(e), then if |x| < d, |x^2sin(1/x)| <= |x|^2*1 < d^2 = e, i'll let you do the rest, but that's the idea though
 
C) looks really hard, I wish I could help you.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
7
Views
2K