anonymous
  • anonymous
Help with limits for a medal?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Jhannybean
  • Jhannybean
No question.
anonymous
  • anonymous
Im attaching the file
anonymous
  • anonymous
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zzr0ck3r
  • zzr0ck3r
Still no question
anonymous
  • anonymous
Use the graph to find the limit and determine the continuity of the function.
anonymous
  • anonymous
Sorry about that. My internet is giving me some troubles.
zzr0ck3r
  • zzr0ck3r
What limit?
zzr0ck3r
  • zzr0ck3r
np the servers here are funny sometimes.
anonymous
  • anonymous
Just a sec. It's not letting me post them
anonymous
  • anonymous
Hah! Got it!
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zzr0ck3r
  • zzr0ck3r
Right, this is what I figured. Ok as you walk along the graph from left to right there is an obvious problem at \(x=-1\). What value do you approach(y value) as you get closer to \(x=-1\)
anonymous
  • anonymous
There's a hole in the graph
zzr0ck3r
  • zzr0ck3r
what value is y when you approach from the left?
anonymous
  • anonymous
2
zzr0ck3r
  • zzr0ck3r
so \(\lim_{x\rightarrow c^{-}}f(x)=2\) What about from the right?
anonymous
  • anonymous
It gets closer to 0
zzr0ck3r
  • zzr0ck3r
Yep so \(\lim_{x\rightarrow 2^{+}}f(x)=0\)
zzr0ck3r
  • zzr0ck3r
now does \(2\ne 0\)?
anonymous
  • anonymous
Yes, 2 doesn't equal zero.
zzr0ck3r
  • zzr0ck3r
obviously not, thus \(\lim_{x\rightarrow c}f(x)\) does not exist
anonymous
  • anonymous
That was much easier than I expected.
zzr0ck3r
  • zzr0ck3r
now, since we cant just fill in one point and make it continuous, i.e. there is no one point that we can add so that we can draw the entire graph without lifting the pencil and thus is does not have a removable discontinuity .
anonymous
  • anonymous
I see now. Thank you! :)
zzr0ck3r
  • zzr0ck3r
np

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