Why are we allowed to do this? v. limits

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

Homework Help Overview

The discussion revolves around the application of limit laws, specifically regarding the limit of the expression lim(e^(lnx)) as x approaches infinity. Participants are questioning the justification for manipulating the limit using the continuity of the exponential function.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the reasoning behind applying continuity in limits, with some suggesting a proof based on limit definitions. Others reference limit laws related to compositions.

Discussion Status

The discussion is ongoing, with participants providing references to limit laws and continuity. There is an exploration of the foundational concepts without a clear consensus on the justification for the manipulation being questioned.

Contextual Notes

One participant notes that this inquiry is not a formal homework problem but rather a point of confusion encountered while reading a textbook, indicating a lack of elaboration on the topic in the source material.

ggcheck
Messages
87
Reaction score
0
lim(e^(lnx)) as x---> inf. = e^(lim(lnx) as x--->inf.)

the book just says "by continuity of e^x"

why are we allowed to do this?
 
Physics news on Phys.org
You can prove it using the definition of a limit. The continuity of e^x turns out to be important in the proof.
 
this isn't an actual homework problem; I ran into this while reading the book... it doesn't elaborate any further
 
Refer back to your limit laws; you learned limits of sums, limits of products, et cetera. One of them was limits of compositions.
 

Similar threads

  • · Replies 22 ·
Replies
22
Views
2K
Replies
5
Views
2K
Replies
2
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
3
Views
1K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
30
Views
3K