I'm reading Understand Calculus and having trouble with one of the questions set after the chapter on finding limits.
The task is to find the limit of f(x) as x approaches 2 when f(x) =
I can tell that in this case the limit is 2 by drawing a graph of the equation, but I think there should also be a way of proving it with algebra. I've tried putting the equation into an online limit finder (Wolfram Alpha) and looking at the working there but it uses l'Hospital's rule and as the book I'm working from hasn't covered that yet (or even toucher on differentiation) I think there is a way to prove the limit without using that rule. Any ideas?