http://prntscr.com/88xfhr ap calc ab

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http://prntscr.com/88xfhr ap calc ab

Mathematics
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HI!!
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
\(-2\) is out, there is no limit there because the function does not even exist to the left of \(-2\)

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Other answers:

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

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