# Thread: Determine following limit: lim x->2 x/(x+2)?

1. ## Determine following limit: lim x->2 x/(x+2)?

Determine following limit: lim x->2 x/(x+2)?

dont know how to go about this one, i know the answer is 1/2 but im not too sure how to go get this answer, could someone show full working, cheers!

2. Originally Posted by hellomoto89
Determine following limit: $lim_ {x \to 2} \frac{x}{x+2}$?

dont know how to go about this one, i know the answer is 1/2 but im not too sure how to go get this answer, could someone show full working, cheers!
Direct substitution. Just replace x with 2.
This fails frequently, but I'm sure you'll let us know when you get to that bridge!

3. There are four basic "rules" for limits:
1) If $\lim_{x\to a} f(x)= F$ and $\lim_{x\to a} g(x)= G$ then $\lim_{x\to a} f(x)+ g(x)= F+ G$
2) If $\lim_{x\to a} f(x)= F$ and $\lim_{x\to a} g(x)= G$ then $\lim_{x\to a}f(x)g(x)= FG$
3) If $\lim_{x\to a} f(x)= F$ and $\lim_{x\to a} g(x)= G$, and $G\ne 0$, then $\lim_{x\to a} \frac{f(x)}{g(x)}= \frac{F}{G}$.
4) If $f(x)= g(x)$ for all x except x= a, then $\lim_{x\to a}f(x)= \lim_{x\to a}g(x)$.

Here, (3) applies.

It's when G= 0 that (3) does not apply, as TheChas said, and then you often can use (4).

You also, of course, need to know the "trivial" limits:
$\lim_{x\to a} C= C$ where C is a constant.
$\lim_{x\to a} x= a$.