Question

Limit of |x-2|/(x-2) as x approaches 2+?

Answer 1

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

Answer 2

yes!

Answer 3

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:
\[\large \lim_{x \rightarrow 2^+}1=1\]

Answer 4

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\(\rightarrow2^+\)

Answer 5

That makes sense now. Thank you! :)

Answer 6

yw