Limit Problem (L'hospitals rule ) (difference)

  • Thread starter Thread starter Seiya
  • Start date Start date
  • Tags Tags
    Difference Limit
Click For Summary
SUMMARY

The discussion centers on solving the limit problem lim x->infinity (x - ln[x]) using L'Hôpital's Rule. Participants confirm that the correct approach involves separately differentiating the numerator and denominator. The user initially attempted to manipulate the expression by substituting x with 1/x^-1, which led to confusion. The consensus emphasizes clarity in differentiation to effectively apply L'Hôpital's Rule.

PREREQUISITES
  • Understanding of L'Hôpital's Rule
  • Familiarity with limits in calculus
  • Knowledge of differentiation techniques
  • Basic logarithmic functions and properties
NEXT STEPS
  • Practice additional limit problems using L'Hôpital's Rule
  • Review differentiation of logarithmic functions
  • Explore advanced limit techniques beyond L'Hôpital's Rule
  • Study the behavior of functions as x approaches infinity
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of limit problems and L'Hôpital's Rule applications.

Seiya
Messages
43
Reaction score
1
Help please =P I've been doing all the l'hospitals rule problems fine and i did the limit of 1/x-cscx fine... same for otehers but i can't get this one??

lim x->infinity (x-ln[x])

I tried making x = 1/x^-1 and then combining them but that made it so confusing, is that the right approach?? :bugeye:

Any advice appreciated. Thank you!
 
Physics news on Phys.org
Your approach works. Just make sure you separately differentiate the fraction in the numerator from the fraction in the denominator.
 

Similar threads

Solving a Limit Problem using L'Hospital Rule
  • · Replies 8 ·
Replies
8
Views
2K
Limit of a fraction as n-> infinity in the numerator and denomominator
  • · Replies 17 ·
Replies
17
Views
2K
Evaluating the Limit of Cosine Function Using L'Hospital's Rule - Explained
  • · Replies 4 ·
Replies
4
Views
2K
Need help finding the limit of a function
  • · Replies 5 ·
Replies
5
Views
2K
Can the limit of a quotient of trig functions approach a specific value?
  • · Replies 2 ·
Replies
2
Views
2K
Using L'Hospital's Rule to Find the Limit of (1+1/n)^n as n Approaches Infinity
  • · Replies 10 ·
Replies
10
Views
2K
L'Hospital's Rule: Understanding and Applying the Rule for Limits at Infinity
  • · Replies 6 ·
Replies
6
Views
2K
Limit as x approaches infinity.
  • · Replies 2 ·
Replies
2
Views
2K
Solving Limits with L'Hospital's Rule
  • · Replies 15 ·
Replies
15
Views
2K
Evaluate the limit as x goes to infinity using L'Hospital's rule
  • · Replies 6 ·
Replies
6
Views
2K