The limit of the expression (ln(x))^2/x as x approaches infinity is a topic of discussion that highlights the application of L'Hôpital's Rule. Participants clarify that the limit can be rewritten as lim (ln(x))^2/x = 5/(x/ln(x)). The confusion arises from the manipulation of the limit and the introduction of an arbitrary constant, 5, which is not justified. The correct approach involves recognizing that as x approaches infinity, the term x/ln(x) also approaches infinity, leading to the conclusion that the limit evaluates to 0.
PREREQUISITESStudents studying calculus, particularly those focusing on limits and L'Hôpital's Rule, as well as educators looking for examples to illustrate these concepts.
Cacophony said:The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
=5/(x/lnx)
How do I calculate x/lnx?
Where did the 5 come from? In fact, where did any of this come from? What you have makes zero sense to me.Cacophony said:Homework Statement
lim (lnx)^2/x
x-->infinity
Homework Equations
none
The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
Cacophony said:=5/(x/lnx)
How do I calculate x/lnx?
Cacophony said:Homework Statement
lim (lnx)^2/x
x-->infinity