Question

Limx->9 abs(9-x)/(9-x)

Answer 1

\[\lim_{x\to 9}\frac{|x-9|}{x-9}\] does not exist for the following reason

Answer 2

Thank you! I thought it didn't exist but wasn't 100% confident in my answer

Answer 3

\[f(x) = \frac{|x-4|}{x-9} = \left\{\begin{array}{rcc}
-1 & \text{if} & x <9 \\
1 &\text{if} & x >9
\end{array}
\right.
\]

Answer 4

oops typo there

Answer 5

\[f(x) = \frac{|x-9|}{x-9} = \left\{\begin{array}{rcc}
-1 & \text{if} & x <9 \\
1 &\text{if} & x >9
\end{array}
\right.\]

Answer 6

so from the left the limit is \(-1\) and form the right the limit is 1