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clara1223

  • one year ago

find the limit as x approaches 1 of abs(x-1)/x-1

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  1. clara1223
    • one year ago
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    \[\lim_{x \rightarrow 1}\frac{ \left| x-1 \right| }{ x-1 }\]

  2. random231
    • one year ago
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    okay what is the first thing you check for when you solve a limit?

  3. dinamix
    • one year ago
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    its 1 or -1

  4. clara1223
    • one year ago
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    @random231 you plug it in to see if you get 0/0

  5. random231
    • one year ago
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    nope dinamix i dont think you got it!

  6. clara1223
    • one year ago
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    @random231 and if so you have to simplify

  7. random231
    • one year ago
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    no clara the first thing you have to check whether the limit exists or not!

  8. jdoe0001
    • one year ago
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    \(\large { \lim\limits_{x\to 1}\ \cfrac{|x-1|}{x-1}\implies \begin{cases} \lim\limits_{x\to 1^{\color{red}{ +}}}\ \cfrac{+(x-1)}{x-1} \\ \quad \\ \lim\limits_{x\to 1^{\color{red}{ -}}}\ \cfrac{-(x-1)}{x-1} \end{cases} }\)

  9. dinamix
    • one year ago
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    \[\lim_{x \rightarrow 1^+} = \frac{ x-1 }{ x-1 } = 1 \]

  10. random231
    • one year ago
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    that is you put in a value immediate to the left of 1 in one case and to the right in the other case. if both of them give the same value then the limit exists.

  11. dinamix
    • one year ago
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    yup @ what i said @random231 its 1 and -1

  12. dinamix
    • one year ago
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    the answer

  13. random231
    • one year ago
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    nope there cant be two values

  14. clara1223
    • one year ago
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    @dinamix if thats the case then doesn't the limit not exist? if theyre two different numbers?

  15. random231
    • one year ago
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    exactly

  16. jdoe0001
    • one year ago
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    notice the values found for the two one-sided limits they differ thus the two-sided limit of \(\lim\limits_{x\to 1}\ \cfrac{|x-1|}{x-1}\impliedby \textit{does not exist}\)

  17. dinamix
    • one year ago
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    |dw:1441065218850:dw| this is graph of function now we understand everything i think i am right about my graph draw it @clara1223 , @random231

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