## anonymous one year ago Limit of |x-2|/(x-2) as x approaches 2+?

1. idku

$\large \lim_{x \rightarrow 2^+}\frac{|x-2|}{x-2}$ like this?

2. anonymous

yes!

3. idku

for all values that are greater than 2, the x-2 is going to be positive anyway without the absolute value). So, you can re-write it as:$\large \lim_{x \rightarrow 2^+}\frac{x-2}{x-2}$ and then: $\large \lim_{x \rightarrow 2^+}1=1$

4. idku

you can graph the function and see how does it behave from the right of x=2, and you will also find out that y=1 when x$$\rightarrow2^+$$

5. anonymous

That makes sense now. Thank you! :)

6. idku

yw