What are some strategies for solving limit problems involving zero or infinity?

  • Context: Undergrad 
  • Thread starter Thread starter gsxrK3
  • Start date Start date
  • Tags Tags
    Couple Limit
Click For Summary
SUMMARY

This discussion focuses on strategies for solving limit problems involving zero and infinity, specifically using L'Hôpital's Rule and the definition of limits. The first problem, lim x->0 of (a^x - b^x)/x, requires applying L'Hôpital's Rule due to the indeterminate form 0/0. The second problem, lim x->9 of (1-x)^(1/x), also presents an indeterminate form, necessitating logarithmic transformation for resolution. The third limit, lim x->infinity [sqrt(x)logx]/x, can be simplified using asymptotic analysis.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hôpital's Rule
  • Knowledge of logarithmic functions and transformations
  • Basic concepts of asymptotic analysis
NEXT STEPS
  • Study L'Hôpital's Rule and its applications in calculus
  • Learn about logarithmic transformations for solving limits
  • Explore asymptotic analysis techniques for evaluating limits at infinity
  • Practice additional limit problems involving indeterminate forms
USEFUL FOR

Students studying calculus, particularly those tackling limit problems involving zero and infinity, as well as educators seeking to enhance their teaching strategies in limit evaluation.

gsxrK3
Messages
4
Reaction score
0
Hello. I have a couple limit problems for my homework and I'm not sure what to do with them.

1. lim x->0 of (a^x - b^x)/x = ?

I see that as x goes to zero, the top goes to 1-1 which would make the whole thing zero, but at the same time the bottom goes to 0 but you can't divide by zero of course. I'm not sure if I'm supposed to do some voodoo to remove the x from the bottom, or if there's some concept I should explain. Maybe I need to use the definition of a limit somehow?

2. lim x->9 of (1-x)^(1/x). Again the same type of situation. 1^(anything) is 1, but at the same time the exponent is going to (1/0).

There is also a third problem. If there is something different I need to know about this I would appreciate some tips, but if you think I can get it once I learn the previous two then never mind it.

3. lim x->infinity [sqrt(x)logx]/x

Thank you,
gsxrk3
 
Physics news on Phys.org
lhopital...sorry for the stupid question.
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 53 ·
2
Replies
53
Views
7K
  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 17 ·
Replies
17
Views
3K