How do I find the one sided limit for the following

Question

anonymous · Answer

$$f(x)=\frac{ \left| x-2 \right| }{ x-2 }$$
find a 
$$\lim_{x \rightarrow 2^{+}} f(x)$$ & b
$$\lim_{x \rightarrow 2^{-}} f(x)$$

anonymous · Answer

you find it as it approaches from one side. if its positive then it is approaching the number from the right side, if it is negative then it approaching the limit from the left side.

raffle_snaffle · Answer

Brake it down for her/him.

anonymous · Answer

go to desmos.com and plug this in the calculator ($\frac{\abs \left(x-2\right)}{x-2}$) and it will graph the function for you.

anonymous · Answer

I was hoping that you would help me by doing the process

raffle_snaffle · Answer

Apply limit laws

anonymous · Answer

@sarcos11 do you know what is a limit in first place? I am sorry I dont know where you stand.

anonymous · Answer

I know what they are, I'm just trying to refresh my memory

anonymous · Answer

so what you do is that you see the value of the number as it approaches a certain x value from a particular side. This is what is meant by a one sided limit. So when you take the limit of a for example, you are actually looking at the limit of the function that approaches x from the positive side. If you graph the function you will notice that it is equal to one. as for b it would equal to -1. In this case the limit of the number doesn't exist because the limit from either sides doesn't approach a definite number. Hope I helped.