anonymous
  • anonymous
||x|| refers to the greatest integer function lim (||x||-x^2) x->3^negative
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
What's \(\|x\|\) for \(x<3\) ?
anonymous
  • anonymous
what does x->3^negative mean
anonymous
  • anonymous
\(x\to3^-\), or "x approaches 3 from the left."

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anonymous
  • anonymous
@HemerickLee, directly substituting works, you just have to consider what the greatest integer function gives you for values of x less than (but close to) 3.
anonymous
  • anonymous
-7 is the answer
anonymous
  • anonymous
But how would you know what the answer is even with the 3-
anonymous
  • anonymous
When u square a number assume it to b a whole no.
anonymous
  • anonymous
\[\lim_{x\to3^-}\left(\|x\|-x^2\right)=\lim_{x\to3^-}\|x\|-\lim_{x\to3^-}x^2\] For the first limit, you find the greatest integer for values of \(x\) less than but close to 3, which would mean \[\|2.9\|=\|2.99\|=\|2.999\|=\cdots=2\]
anonymous
  • anonymous
Ok, then what would we have to do next
anonymous
  • anonymous
The other limit is pretty clear. \(x^2=9\) when \(x\to3\). So 2-9 is?
anonymous
  • anonymous
-7................................. But for the first one then it would be 2 and the second on it would be -7 but then what would it be to the left
anonymous
  • anonymous
-7 .... as simple... dats wot i wrote earlier
anonymous
  • anonymous
I know but I needed to know how to work through it. Thank you @frnd and @SithsAndGiggles
anonymous
  • anonymous
welcome dear HemerickLee

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