Question

limit of |x-2\/x-2 as x approaches 2. would the limit be 0?

Answer 1

so it looks like your function is a little messed up

Answer 2

not clear to me what the function is.

Answer 3

ill write it out better hold on

Answer 4

\[\lim_{x \rightarrow 2}\frac{|x-2|}{x-2}\] ?

Answer 5

aaah i thought as much. no limit

Answer 6

yeah you are correcy myinninaya.

Answer 7

correct*

Answer 8

this is a piecewise function. it is 1 if x > 2, -1 if x < 2

Answer 9

\[x>2=>|x-2|=x-2, x<2=>|x-2|=-(x-2)\]

Answer 10

and so the limit from the right is 1, the limit from the left is -1, and since those numbers are not the same the limit does not exist

Answer 11

\[\lim_{x \rightarrow 2^-}\frac{-(x-2)}{x-2}=-1\]

Answer 12

\[\lim_{x \rightarrow 2^+}\frac{x-2}{x-2}=1\]

Answer 13

oh ok yeah i made a table and i got those results, but i wasnt sure if there was a limit or not. i have to write why, but im not quite sure of the reason.

Answer 14

\[\lim_{x \rightarrow 2}\frac{|x-2|}{x-2} DNE\]

Answer 15

\[f(x) = \frac{|x-2|}{x-2} = \left\{\begin{array}{rcc}
1 & \text{if} & x \geq 2 \\
-1& \text{if} & x < 2
\end{array}
\right.\]

Answer 16

tada!

Answer 17

do you know if we have |x|,
then:
x>0 => |x|=x

x<0 => |x|=-x

x=0 => |x|=0

Answer 18

why is it writing everything on one line :(

Answer 19

hmmm.
?