Why is it that I need to change the variable n to x before I apply L'hôpitals rule to an equation?

Question

anonymous · Answer

Example:

anonymous · Answer

I'm bringing it up to find out why because my professor had also mentioned it, as well.

loser66 · Answer

because $a_n$ is a sequence , the graph of it is a set of dot $\bullet$, it's not a continuous function or a function itself, therefore, we have to use the correspondent function to "turn" it to a function to consider where it goes, converse or diverge, 
for example, if you have $a_n = n^2 +1$ when n =1, $a_n =2$ and so on, you don't have a parabola, you just have something like|dw:1380846909426:dw|

loser66 · Answer

but when you apply the "similar" function of x^2 +1 you have |dw:1380846989998:dw|