The discussion revolves around calculating limits involving natural logarithms as \( x \) approaches infinity. Participants are exploring two specific limits: \( \lim_{x \to \infty} \frac{(\ln x)^5}{x} \) and \( \lim_{x \to \infty} \frac{14 \ln x^2}{6 \ln x^3} \). There is a focus on understanding the behavior of logarithmic functions in these limits.
The discussion is active, with participants providing different insights and suggestions. Some have offered guidance on using logarithmic properties, while others are questioning assumptions and the correctness of previous attempts. There is no explicit consensus on the final outcomes, but several participants are engaging with the problems constructively.
One participant mentions a restriction against using L'Hôpital's rule, which influences the approaches being considered. There is also a mention of confusion regarding the application of derivatives in the context of limits.
You're going in circles... back to what you started with.Cacophony said:Homework Statement
I'm having trouble calculating these limits.
Homework Equations
none
The Attempt at a Solution
1. lim...((lnx)^5)/(x)=
x->infinity
(((lnx)^5)/x)/(x/x)=
(((lnx)^5)/x)/1=
How do I calculate from here?
In #2, what you have done is incorrect.2.lim ...(14lnx^2)/(6lnx^3)=
x->infinity
((14lnx^2)/(x^3))/((6lnx^3)/(x^3))=
((14lnx)/(x))/(6lnx)=
0/6lnx= 0
Is this right or am I forgetting something?
If you mean the limit of 28lnx/(18lnx), then yes, that's right.Cacophony said:So would the second problem look something like this:
28lnx/18lnx?
A limit of the form 0/0 is indeterminate. It might exist or might not exist.Cacophony said:ok so it will be ((28lnx)/x)/((18lnx)/x) = 0/0 = DNE?
Yes !Cacophony said:1/1 ?
Yes.Cacophony said:So basically the limit is then 28/18?