## math456 3 years ago Did i do this correctly??

1. math456

2. jldstuff393

i can't quite read c is that x approaching 1-?

3. math456

its just 1

4. jldstuff393

then what does a say?

5. math456

lim of f(x) as x approaches to 1

6. jldstuff393

so its the same equation? a and c are both lim as x->1 of f(x)?

7. math456

a is x->1-

8. jldstuff393

oh ok. well yes A is correct. if b is x->x+ then it it is also correct, that limit does not exist. c is also correct, but d and e are incorrect...any idea why?

9. math456

d doesn't exit because of the knot!

10. math456

ohhh wait, but from the left hand and right hand side its meeting at 4

11. jldstuff393

u mean the hole in the graph?

12. jldstuff393

yes

13. math456

so it does exist

14. jldstuff393

yep. f(5) doesn't have to be defined to have a limit there.. as long as it approaches the same number from both sides, it exists

15. jldstuff393

16. math456

wait ur 2nd last comment was on option d right!

17. jldstuff393

well ya but i kind of gave away the answer to e, too, i think hah

18. jldstuff393

but yes, for d, the limit as x->5 of f(x) exists because the function obviously approaches 4 at f(5).

19. math456

kool!

20. math456

so wht does it means if we hv a knot in the graph! why is it undef??

21. phi

btw, the question asks for the value of the limit when it exists (not just that it exists)

22. math456

like for b its undefined,

23. math456

lol thanks @phi so u tell me if its right a) 2 b) 3 c) dne d) 4 e) dne

24. jldstuff393

oh i'm sorry. ur right on b. that is defined since it's just coming from the right.

25. jldstuff393

so a and b are both defined and c is undefined

26. jldstuff393

d is also defined like we just talked about, but what about e?

27. math456

does it means that the y value is 5?

28. jldstuff393

well f(5) is asking what y is equal to when x=5

29. phi

an open circle means that value is not defined. note that (e) is not a limit problem

30. math456

so e) is 4

31. jldstuff393

so if you look on the graph where x = 5, the there's a hole, meaning y is undefined

32. jldstuff393

it basically skips over that one point. it approaches it from both sides, but y never equals 4 because theres that hole there

33. math456

ohh okay got it now!

34. jldstuff393

cool. so it doesn't exist, right?

35. math456

no like u said coz of the hole!

36. jldstuff393

yup :)

37. math456

okay thanks for ur help guys!

38. jldstuff393

sure! the question also asks for the value of the quantity, if it exists

39. phi

btw, if (b) is x-> 1+ (approaching from the right), the limit does not exist

40. math456

yea i asked @phi if i did it right!

41. math456

okay so a) 2 b) dne c) dne d) 4 e) dne, correct?

42. jldstuff393

umm i could be wrong but i thought b exists

43. jldstuff393

i actually wasn't sure so i looked it up, i'm seeing examples of limits approaching an undefined, discontinuous point from one side that exist

44. jldstuff393

phi, u here?

45. math456

umm okay

46. jldstuff393

but aside from that, i agree w ur answers, but i think b exists and it's 3

47. math456

i m still confused on b!

48. math456

coz from the left its 1 and it exist why it doesn't exist from the other side?

49. math456

2*

50. jldstuff393

exactly...i think it does exist from the other side. i think phi's wrong

51. math456

well i guess i hv to look for the difference btw the hole vs black hole!

52. jldstuff393

definitely. black (filled in) means f(x) is defined at that point, hole (empty) means its not

53. math456

there u go so it doesn't exist coz its empty

54. jldstuff393

exactly. unless there's a black point somewhere randomly off the graph at the same x as the hole, then it's defined, just not continuous

55. phi

do you have a link? see example http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx

56. jldstuff393

idk if you've covered continuity yet, tho hah, so i don't want to add extra confusion.

57. jldstuff393

phi why do you think b doesn't exist?

58. phi

for(b) I can not read the problem, but if you are approaching x=1 from the left the limit defined. If you approach right to left, the limit is undefined.

59. jldstuff393

it is right to left. hmm

60. phi

61. jldstuff393

in example 1 of the link, there's no mention of right-hand or left-hand limits...

62. math456

i agree!!

63. jldstuff393

that's a really good tutorial tho

64. phi

I take it back. That first example was for continuity Here http://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx example 4 , letters (f) and (g) show that one-sided limits exist. so (b) is 3

65. jldstuff393

hah phew. I also first thought that b didn't exist haha but I checked and i was wrong.

66. jldstuff393

so yes, b is 3

67. phi

Obviously I needed a refresher on this stuff.

68. math456

alright so we all agree now b is 3!!

69. jldstuff393

i'm retaking calc 2 right now and am having to relearn everything after precalc, so i understand!

70. jldstuff393

and yes, we agree

71. math456

thanks all!!

72. jldstuff393

speaking of, phi, do you wanna try helping me with my own limit problem?

73. jldstuff393

yw!

74. jldstuff393

i've never used this site... but i really like teaching people so i'm enjoying it...even tho no one's even tried to answer my question :(

75. math456

same here.. and ur question is kinda hard thts y nobody is willing to try!

76. jldstuff393

lol my teacher's impossible! at the tutoring center in my college, sometimes professors come in and look at the problem and say, that's too hard, i dont want to help you with that

77. math456

lol for real!! FAIL.. -_-

78. jldstuff393

yup. not to me personally but it happened to my friend. the professor was like the dean of the math department, too haha

79. jldstuff393

in his defense, tho, he's a stats guy, not calculus

80. math456

hmm but still. Stats is pretty much like math!