## tmagloire1 one year ago http://prntscr.com/88xfhr ap calc ab

1. misty1212

HI!!

2. 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

3. misty1212

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

4. misty1212

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

5. tmagloire1

@misty1212 no it doesn't

6. misty1212

actually it does

7. tmagloire1

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

8. misty1212

it is not continuous at $$x=-1$$ but it does have a limit

9. misty1212

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

10. tmagloire1

oh would it be -1

11. misty1212

yes

12. misty1212

definitely continuous and so has a limit at $$x=0$$ right?

13. misty1212

but not at $$1$$

14. tmagloire1

yep at 0 the limit is 0

15. misty1212

yes

16. tmagloire1

at 2 it is 2

17. tmagloire1

there is no limit at 3

18. misty1212

no there is no limit at 3

19. misty1212

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

20. tmagloire1

it does exist at four as well

21. misty1212

yes it does

22. tmagloire1

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

23. misty1212

looks good to me

24. tmagloire1

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

25. misty1212

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