Finding a limit with the natural log function

Click For Summary
SUMMARY

The discussion focuses on evaluating the limit of the expression \(\lim_{h \to \infty} \frac{\ln(2+h) - \ln(2)}{h}\). Participants clarify that the limit should be taken as \(h\) approaches infinity, not \(x\). The use of l'Hôpital's Rule is recommended to resolve the limit, as it applies to indeterminate forms. The conversation emphasizes the importance of correctly identifying the variable approaching infinity in limit expressions.

PREREQUISITES
  • Understanding of limit notation and concepts
  • Familiarity with natural logarithm properties
  • Knowledge of l'Hôpital's Rule for evaluating limits
  • Basic calculus concepts, particularly difference quotients
NEXT STEPS
  • Study the application of l'Hôpital's Rule in various limit problems
  • Explore the properties of logarithmic functions in calculus
  • Practice evaluating limits involving difference quotients
  • Learn about indeterminate forms and their resolutions in calculus
USEFUL FOR

Students studying calculus, educators teaching limit concepts, and anyone looking to deepen their understanding of logarithmic limits and their applications.

fiziksfun
Messages
77
Reaction score
0
i need help with this:

lim x->[tex]\infty[/tex] of [tex]\frac{ln(2+h) - ln(2)}{h}[/tex]

i have no idea where to even begin!
i tried resolving it, but it didn't help :[

any suggestions??
 
Physics news on Phys.org
That looks funny for several reasons. You've got x->infinity and there are no x's in the limit expression. If you mean h->infinity, then it still looks funny because the limit expression is a difference quotient where you usually take h->0. But if you really mean h->infinity then you can use l'Hopital's rule.
 
ln(a/b)= ??
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 44 ·
2
Replies
44
Views
5K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 19 ·
Replies
19
Views
2K