Limit of a sequence: L'Hopital's rule applied to $(\ln n)/n$

I discuss and solve an example of a limit of a sequence where L'Hopital's rule is applied. The particular sequence is $(\ln n)/n$. This type of example is seen in 1st-year university mathematics. Note that I have used a 'big nib marker' to make everything clearer in full screen mode!

Category:

Education

Tags:

• limit
• sequence
• L'Hopital
• calculus
• analysis
• Chris
• Tisdell
• UNSW
• $(\ln
• n)/n$

[hidjiz]

Thanks!

[Comunista85]

good job

[kayra2011]

muchas gracias =)

[shihitosan]

Thank you very much :)

[Saladin15]

I'm just happy people can devote their time to helping others.

[haxdwawin]

Many thanks from Poland for this solution of such a simple problem :)) Nice job.

[Artopunk14]

Thanks for this DrChrisTisdell

[mikebr203]

@10493566

It would be 1/0 if it was asked for the limit as x approaches 0. The sequence of numbers as x approaches infinity is (1,1/2,1/3,1/4....). Notice that they're getting closer and closer to zero.

[10493566]

Thank you but im still a but confused. If lim as x aproches infinity is the quantity of (1/x)/1 wouldn't that be the same as 1/x. So when you substitute infinity in wouldn't that be 1/0 not 0/1. So instead would it be undefined, and the limit does not exist?

[lutetium1907]

thanks for you vdo , i'm subscribing