tmagloire1
  • tmagloire1
http://prntscr.com/88xfhr ap calc ab
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
we have to check to see if a limit exists at a bunch of numbers right?\[\{-2,-1,0,1,2,3,4,5\}\] so it is going to take a while to do them all
misty1212
  • misty1212
\(-2\) is out, there is no limit there because the function does not even exist to the left of \(-2\)

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misty1212
  • misty1212
how about \(-1\)? does the function have a limit as \(x\to -1\)?
tmagloire1
  • tmagloire1
@misty1212 no it doesn't
misty1212
  • misty1212
actually it does
tmagloire1
  • tmagloire1
But doesn't the hole mean it's discontinuous at that point?
misty1212
  • misty1212
it is not continuous at \(x=-1\) but it does have a limit
misty1212
  • misty1212
right, but it is not asking for "continuous" it is asking if the limit exists
tmagloire1
  • tmagloire1
oh would it be -1
misty1212
  • misty1212
yes
misty1212
  • misty1212
definitely continuous and so has a limit at \(x=0\) right?
misty1212
  • misty1212
but not at \(1\)
tmagloire1
  • tmagloire1
yep at 0 the limit is 0
misty1212
  • misty1212
yes
tmagloire1
  • tmagloire1
at 2 it is 2
tmagloire1
  • tmagloire1
there is no limit at 3
misty1212
  • misty1212
no there is no limit at 3
misty1212
  • misty1212
at 2 it is not 2, it is somewhat less than 2, but the limit does exist there
tmagloire1
  • tmagloire1
it does exist at four as well
misty1212
  • misty1212
yes it does
tmagloire1
  • tmagloire1
so overall there is a limit at -1,0,2, and 4
misty1212
  • misty1212
looks good to me
tmagloire1
  • tmagloire1
Alright, thank you for the help, sorry i took so long responding my internet went out!
misty1212
  • misty1212
\[\color\magenta\heartsuit\](you did most of it yourself!)

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