LifeIsADangerousGame
  • LifeIsADangerousGame
Calculus
Mathematics
katieb
  • katieb
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LifeIsADangerousGame
  • LifeIsADangerousGame
\[\lim_{x \rightarrow 2} \frac{ \left| x - 2 \right| }{ x - 2 }\]
welshfella
  • welshfella
the limit will be different for x approaching 2 from above and that for x approaching 2 from below. Because the numerator will always be positive ( absolute value)
welshfella
  • welshfella
Limits are not my strong point I'm afraid

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welshfella
  • welshfella
My guess is that the limit is 1 for x approaching above 2 , and -1 for x approaching from below 2. But i'm not sure.
LifeIsADangerousGame
  • LifeIsADangerousGame
That's what the calculator I used says, I just don't know how to show my work for it.
johnweldon1993
  • johnweldon1993
May not be your strong point, however you are correct @welshfella :) As you said, the limit = -1 as we approach 2 from the left And the limit = 1 as we approach 2 from the right Since there are 2 different values, the limit does not exist
welshfella
  • welshfella
Right - i cant help you there.
johnweldon1993
  • johnweldon1993
Its easy to show, Instead of putting in 2 for 'x' Plug in 1.99999 for 'x' to show what the answer would be if we approach 2 from JUST below it And plug in 2.00001 for 'x' to show what it would be if we approach 2 from JUST above it
welshfella
  • welshfella
- yes - I had something like that in my mind also.
LifeIsADangerousGame
  • LifeIsADangerousGame
Thank you both!

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