Science talk:Math Exam Resources/Courses/MATH101/April 2011/Question 8

What is going on?! |x-2|<1 is not the same as |x|<3.

Agree. Also, dividing by $ln(1)$ is not very cool either...

I fixed these errors, but left out some minor details. Somebody might want to fill them in. (For example, I did comment out a proof that \ln(n+2)/\ln(n+3) \to 1 as n\to \infty because I think it was too long-winded for something so obvious, but it could be uncommented and cleaned up as well.)

So this limit is 'obvious' but not really - its actually tricky to give a correct proof without using L'hopital's rule. The way I managed to do it was to use a change of variables with m = n+3. Someone should fill this in.

Well, I don't find it too tricky, but anyway, I uncommented a proof as requested.

Can't we use l'Hospital rule?

Of course, L'Hopital's rule applies here, but I've gathered from students in the Tutorial Centre that they are (surprisingly and unfortunately) not learning this in their calculus classes here at UBC. If this is indeed the case, then we should probably avoid referring to it in our solutions.