Determine if the sequence convergence and if so, find the limit

Question

anonymous · Answer

$$a_n = \frac{3+5n^2}{n+n^2}$$

The limit is inf/inf.  May we do L'hospital's rule?  (I've read somewhere that it may not be used since the a_n formula isn't really a function f(x))

terenzreignz · Answer

Yes... but the function 
$$\Large f(x) = \frac{3+5x^2}{x+x^2}$$ certainly converges to a limit as x tends to infinity...

If that goes to that limit, why not the sequence? :)

anonymous · Answer

So, may I just replace all n's with x's each time and use that as f(x)?

terenzreignz · Answer

Yeah... if they have a limit, they have to be the same, right?

anonymous · Answer

Yeah that actually makes sense.
Well I got the answer as 5


But why do they say you can't do lim on a_n?    That will never be needed since x can be replaced with x?