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