onegirl 2 years ago Help please? state the limit and if there is not limit say that limit doesn't exist.

1. onegirl

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. onegirl

3. onegirl

@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. onegirl

hmm ok

7. onegirl

so for the first one it will be -2?

8. onegirl

soo?

9. UnkleRhaukus

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

10. onegirl

ohh okay

11. onegirl

so the limit will be zero?

12. UnkleRhaukus

yeah for the first one thats right

13. onegirl

okay

14. onegirl

lemme try the second one

15. onegirl

so number 2 will be -1? right?

16. UnkleRhaukus

correct

17. onegirl

ohh i think i'm starting to get this

18. onegirl

hmm for number 3 will the open circle count?

19. onegirl

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. onegirl

so it will be positive 2?

23. UnkleRhaukus

um check that again

24. onegirl

ok

25. onegirl

positive 1?

26. onegirl

wait it will be -2

27. onegirl

did i get it?

28. UnkleRhaukus

nope

29. onegirl

okay i'm gonna try again

30. onegirl

it will be -3

31. UnkleRhaukus

how could it be negative?

32. onegirl

oh imeant positive 3

33. onegirl

so is that correct?

34. UnkleRhaukus

thats better

35. onegirl

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. onegirl

okay number 5 will be -2?

38. UnkleRhaukus

nope

39. onegirl

hmmm ohh ok so it will be undefined right?

40. UnkleRhaukus

im not sure how you are getting that/

41. onegirl

let me look it again

42. onegirl

it will be positive 2?

43. onegirl

am i right?

44. UnkleRhaukus

it looks more like 1.5 to me

45. onegirl

its close but it hasn't reached the line

46. onegirl

ok

47. onegirl

how about the last one? its tricky

48. UnkleRhaukus

what do you think

49. onegirl

it will be it doesnt exist

50. onegirl

right?

51. UnkleRhaukus

why would you say that

52. onegirl

hmmm hold on

53. onegirl

it will be 3?

54. onegirl

did i get it?

55. UnkleRhaukus

a bit less

56. onegirl

2?

57. onegirl

soo?

58. onegirl

are u there?

59. UnkleRhaukus

dosent look like 2 to me

60. UnkleRhaukus

look like about 2.5 to me

61. onegirl

ok thanks