Question

Find the following limit if it exist. limit as x approaches 6 from positive side of abs(x-6)

Answer 1

\(\Large lim_{x\to 6}\quad |x-6|\to
\begin{cases}
lim_{x\to 6^+}\quad +(x+6)
\\ \quad \\
lim_{x\to 6^-}\quad -(x+6)
\end{cases}\)

Answer 2

so test the first case then

Answer 3

why did you change the sign inside the bracket from (x-6) to (x+6)?

Answer 4

ohh yeas I did.. shootr... typo

Answer 5

\(\Large lim_{x\to 6}\quad |x-6|\to
\begin{cases}
lim_{x\to 6^+}\quad +(x-6)
\\ \quad \\
lim_{x\to 6^-}\quad -(x-6)
\end{cases}\)

Answer 6

could you please solve it...thanks!

Answer 7

well... there isn't much to solve really

just make "x" reach the limit

you just need to solve the 1st one-sided limits

Answer 8

okay so if x reaches the limit we get zero from both positive and negative side...right?

Answer 9

hmm nope, we do from one of them, yes, not for both

Answer 10

hmm actually wait a sec... nope, you're correct

Answer 11

okay. same question lim as x approaches 0 for abs(x)/x

Answer 12

i am confused because in my original question the answer is zero but in this question the answer is not zero it is +1 and -1 therefore the limit does not exist

Answer 13

hmm... maybe ... .something is missing in the ..... posting

Answer 14

I read \(\Large lim_{x\to 0}\quad |x-6|\)

Answer 15

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJhYnMoeC02KSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0zLjc2IiwiOS4yNCIsIi0zLjk4IiwiNC4wMiJdfV0- <--- you can pretty much see is 0

Answer 16

actually its a question with multiple parts. I will attach an image from my book.

Answer 17

hmm maybe simpler to post anew with the full material.....thus if I dunno someone else may

Answer 18

okay..I will post a new question but thanks for your help :)