Find the limit of (sqrt(1+2x) - sqrt(1+3x))/(x + 2x^2) as x->0

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

Homework Help Overview

The discussion revolves around finding the limit of the expression (sqrt(1+2x) - sqrt(1+3x))/(x + 2x^2) as x approaches 0. This involves concepts from calculus, specifically limits and potentially the application of L'Hôpital's Rule or algebraic manipulation techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest various methods to tackle the limit, including the use of L'Hôpital's Rule and multiplying by the conjugate of the numerator. There is also a mention of checking numerical values to gain insight into the limit's behavior.

Discussion Status

The discussion is active, with multiple approaches being proposed. Some participants emphasize the importance of understanding whether L'Hôpital's Rule is applicable based on prior learning. There is no explicit consensus on a single method to pursue, but several viable strategies are being explored.

Contextual Notes

There is a mention of potential constraints regarding the teaching of L'Hôpital's Rule, which may affect the approaches participants are willing to consider. Additionally, the numerical testing of values is suggested as a supplementary method to understand the limit's behavior.

kreil
Science Advisor
Insights Author
Messages
665
Reaction score
68
I'm having a lot of trouble making any progress on this limit. If someone could give me a direction to get started I would appreciate it.

\lim_{x{\rightarrow}0}\frac{\sqrt{1+2x}-\sqrt{1+3x}}{x+2x^2}
 
Physics news on Phys.org
Use L'Hopitals Rule.
 
Or you could multiply by the conjugate of the numerator. (ie, sqrt(1+2x)+sqrt(1+3x)).
 
Go with StatusX's advice if l'hospital's Rule wasn't taught yet because then it wouldn't be appropriate.

If you haven't learned l'hospital's Rule, I recommend to learn it and use it to check your answer

Also, you can always test it numerically. I do that sometimes just to be 100% certain. I would try something like x=0.01, 0.001 and 0.0001.
 
As stated above, L'Hopital's rule, or, if that's not allowed, rationalize the numerator.
 

Similar threads

  • · Replies 105 ·
4
Replies
105
Views
8K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 44 ·
2
Replies
44
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K