## anonymous 3 years ago Help please? state the limit and if there is not limit say that limit doesn't exist.

1. anonymous

1) lim x-> -1 f(x) 2) lim x-> 2- f(x) 3) lim x-> 2+ f(x) 4) lim x-> 2 f(x) 5) lim x-> -2 f(x) 6) lim x-> 3f(x)

2. anonymous

3. anonymous

@UnkleRhaukus can u help?

4. UnkleRhaukus

$\lim\limits_{ x\to -1} f(x)$ is the height of the blue line above x=-1 on the x-axis

5. UnkleRhaukus

$\lim\limits_{ x\to 2^-} f(x)$ is the height of the blue line above the point just before 2 on the x axis

6. anonymous

hmm ok

7. anonymous

so for the first one it will be -2?

8. anonymous

soo?

9. UnkleRhaukus

no. the blue line is crossing the axis at x=-1, so the height is zero here

10. anonymous

ohh okay

11. anonymous

so the limit will be zero?

12. UnkleRhaukus

yeah for the first one thats right

13. anonymous

okay

14. anonymous

lemme try the second one

15. anonymous

so number 2 will be -1? right?

16. UnkleRhaukus

correct

17. anonymous

ohh i think i'm starting to get this

18. anonymous

hmm for number 3 will the open circle count?

19. anonymous

or will it be undefined?

20. UnkleRhaukus

$\lim\limits_{ x\to 2^+} f(x)$ is where x is a little bit to the right of 2 so is a tiny bit to the right of the open circle

21. UnkleRhaukus

if you were looking for the limit as $x\to 2$ and both circles were open then it would be undefined

22. anonymous

so it will be positive 2?

23. UnkleRhaukus

um check that again

24. anonymous

ok

25. anonymous

positive 1?

26. anonymous

wait it will be -2

27. anonymous

did i get it?

28. UnkleRhaukus

nope

29. anonymous

okay i'm gonna try again

30. anonymous

it will be -3

31. UnkleRhaukus

how could it be negative?

32. anonymous

oh imeant positive 3

33. anonymous

so is that correct?

34. UnkleRhaukus

thats better

35. anonymous

ok so number 4 will be -1 ?

36. UnkleRhaukus

thats right, ( note that if the lower circle was open then it would be undefined)

37. anonymous

okay number 5 will be -2?

38. UnkleRhaukus

nope

39. anonymous

hmmm ohh ok so it will be undefined right?

40. UnkleRhaukus

im not sure how you are getting that/

41. anonymous

let me look it again

42. anonymous

it will be positive 2?

43. anonymous

am i right?

44. UnkleRhaukus

it looks more like 1.5 to me

45. anonymous

its close but it hasn't reached the line

46. anonymous

ok

47. anonymous

how about the last one? its tricky

48. UnkleRhaukus

what do you think

49. anonymous

it will be it doesnt exist

50. anonymous

right?

51. UnkleRhaukus

why would you say that

52. anonymous

hmmm hold on

53. anonymous

it will be 3?

54. anonymous

did i get it?

55. UnkleRhaukus

a bit less

56. anonymous

2?

57. anonymous

soo?

58. anonymous

are u there?

59. UnkleRhaukus

dosent look like 2 to me

60. UnkleRhaukus

look like about 2.5 to me

61. anonymous

ok thanks