Question

what is the absolute value of (x-2)/(x-2) limit 2

Answer 1

\[\frac{x-2}{x-2}=1\] for all \(x\) except \(x=2\) so the limit is \(1\)

Answer 2

oooh i bet it is this
\[\frac{|x-2|}{x-2}\] am i right?

Answer 3

no the absolute sign is at the bottom

Answer 4

at the bottom but not at the top?

Answer 5

yes that's correct

Answer 6

ok then
\[\frac{x-2}{|x-2|}\] is really only two numbers
if \(x>2\) it is \(\frac{x-2}{x-2}=1\)
but if \(x<2\) you have \(\frac{x-2}{|x-2|}=\frac{x-2}{-x+2}=-1\)

Answer 7

in other words, it is a fancy way of writing
\[f(x) = \left\{\begin{array}{rcc}
-1 & \text{if} & x <2\\
1& \text{if} & x >2
\end{array}
\right.
\]

Answer 8

since evidently \(-1\neq 1\) this limit is undefined

Answer 9

can you please show me the workings, what I am seeing is only the answer

Answer 10

can you not see what i wrote?

Answer 11

if you refresh your browser you should be able to see that math that i wrote if you cannot see it now

Answer 12

thank you

Answer 13

yw