Question

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

Answer 1

HI!!

Answer 2

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

Answer 3

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

Answer 4

how about \(-1\)? does the function have a limit as \(x\to -1\)?

Answer 5

@misty1212 no it doesn't

Answer 6

actually it does

Answer 7

But doesn't the hole mean it's discontinuous at that point?

Answer 8

it is not continuous at \(x=-1\) but it does have a limit

Answer 9

right, but it is not asking for "continuous" it is asking if the limit exists

Answer 10

oh would it be -1

Answer 11

yes

Answer 12

definitely continuous and so has a limit at \(x=0\) right?

Answer 13

but not at \(1\)

Answer 14

yep at 0 the limit is 0

Answer 15

yes

Answer 16

at 2 it is 2

Answer 17

there is no limit at 3

Answer 18

no there is no limit at 3

Answer 19

at 2 it is not 2, it is somewhat less than 2, but the limit does exist there

Answer 20

it does exist at four as well

Answer 21

yes it does

Answer 22

so overall there is a limit at -1,0,2, and 4

Answer 23

looks good to me

Answer 24

Alright, thank you for the help, sorry i took so long responding my internet went out!

Answer 25

\[\color\magenta\heartsuit\](you did most of it yourself!)