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math456

  • 2 years ago

Did i do this correctly??

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  1. math456
    • 2 years ago
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  2. jldstuff393
    • 2 years ago
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    i can't quite read c is that x approaching 1-?

  3. math456
    • 2 years ago
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    its just 1

  4. jldstuff393
    • 2 years ago
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    then what does a say?

  5. math456
    • 2 years ago
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    lim of f(x) as x approaches to 1

  6. jldstuff393
    • 2 years ago
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    so its the same equation? a and c are both lim as x->1 of f(x)?

  7. math456
    • 2 years ago
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    a is x->1-

  8. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    d doesn't exit because of the knot!

  10. math456
    • 2 years ago
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    ohhh wait, but from the left hand and right hand side its meeting at 4

  11. jldstuff393
    • 2 years ago
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    u mean the hole in the graph?

  12. jldstuff393
    • 2 years ago
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    yes

  13. math456
    • 2 years ago
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    so it does exist

  14. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    so what about e?

  16. math456
    • 2 years ago
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    wait ur 2nd last comment was on option d right!

  17. jldstuff393
    • 2 years ago
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    well ya but i kind of gave away the answer to e, too, i think hah

  18. jldstuff393
    • 2 years ago
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    but yes, for d, the limit as x->5 of f(x) exists because the function obviously approaches 4 at f(5).

  19. math456
    • 2 years ago
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    kool!

  20. math456
    • 2 years ago
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    so wht does it means if we hv a knot in the graph! why is it undef??

  21. phi
    • 2 years ago
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    btw, the question asks for the value of the limit when it exists (not just that it exists)

  22. math456
    • 2 years ago
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    like for b its undefined,

  23. math456
    • 2 years ago
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    lol thanks @phi so u tell me if its right a) 2 b) 3 c) dne d) 4 e) dne

  24. jldstuff393
    • 2 years ago
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    oh i'm sorry. ur right on b. that is defined since it's just coming from the right.

  25. jldstuff393
    • 2 years ago
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    so a and b are both defined and c is undefined

  26. jldstuff393
    • 2 years ago
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    d is also defined like we just talked about, but what about e?

  27. math456
    • 2 years ago
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    does it means that the y value is 5?

  28. jldstuff393
    • 2 years ago
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    well f(5) is asking what y is equal to when x=5

  29. phi
    • 2 years ago
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    an open circle means that value is not defined. note that (e) is not a limit problem

  30. math456
    • 2 years ago
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    so e) is 4

  31. jldstuff393
    • 2 years ago
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    so if you look on the graph where x = 5, the there's a hole, meaning y is undefined

  32. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    ohh okay got it now!

  34. jldstuff393
    • 2 years ago
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    cool. so it doesn't exist, right?

  35. math456
    • 2 years ago
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    no like u said coz of the hole!

  36. jldstuff393
    • 2 years ago
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    yup :)

  37. math456
    • 2 years ago
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    okay thanks for ur help guys!

  38. jldstuff393
    • 2 years ago
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    sure! the question also asks for the value of the quantity, if it exists

  39. phi
    • 2 years ago
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    btw, if (b) is x-> 1+ (approaching from the right), the limit does not exist

  40. math456
    • 2 years ago
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    yea i asked @phi if i did it right!

  41. math456
    • 2 years ago
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    okay so a) 2 b) dne c) dne d) 4 e) dne, correct?

  42. jldstuff393
    • 2 years ago
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    umm i could be wrong but i thought b exists

  43. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    phi, u here?

  45. math456
    • 2 years ago
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    umm okay

  46. jldstuff393
    • 2 years ago
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    but aside from that, i agree w ur answers, but i think b exists and it's 3

  47. math456
    • 2 years ago
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    i m still confused on b!

  48. math456
    • 2 years ago
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    coz from the left its 1 and it exist why it doesn't exist from the other side?

  49. math456
    • 2 years ago
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    2*

  50. jldstuff393
    • 2 years ago
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    exactly...i think it does exist from the other side. i think phi's wrong

  51. math456
    • 2 years ago
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    well i guess i hv to look for the difference btw the hole vs black hole!

  52. jldstuff393
    • 2 years ago
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    definitely. black (filled in) means f(x) is defined at that point, hole (empty) means its not

  53. math456
    • 2 years ago
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    there u go so it doesn't exist coz its empty

  54. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    do you have a link? see example http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx

  56. jldstuff393
    • 2 years ago
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    idk if you've covered continuity yet, tho hah, so i don't want to add extra confusion.

  57. jldstuff393
    • 2 years ago
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    phi why do you think b doesn't exist?

  58. phi
    • 2 years ago
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    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
    • 2 years ago
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    it is right to left. hmm

  60. phi
    • 2 years ago
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    see the link, example 1

  61. jldstuff393
    • 2 years ago
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    in example 1 of the link, there's no mention of right-hand or left-hand limits...

  62. math456
    • 2 years ago
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    i agree!!

  63. jldstuff393
    • 2 years ago
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    that's a really good tutorial tho

  64. phi
    • 2 years ago
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    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
    • 2 years ago
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    hah phew. I also first thought that b didn't exist haha but I checked and i was wrong.

  66. jldstuff393
    • 2 years ago
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    so yes, b is 3

  67. phi
    • 2 years ago
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    Obviously I needed a refresher on this stuff.

  68. math456
    • 2 years ago
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    alright so we all agree now b is 3!!

  69. jldstuff393
    • 2 years ago
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    i'm retaking calc 2 right now and am having to relearn everything after precalc, so i understand!

  70. jldstuff393
    • 2 years ago
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    and yes, we agree

  71. math456
    • 2 years ago
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    thanks all!!

  72. jldstuff393
    • 2 years ago
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    speaking of, phi, do you wanna try helping me with my own limit problem?

  73. jldstuff393
    • 2 years ago
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    yw!

  74. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    same here.. and ur question is kinda hard thts y nobody is willing to try!

  76. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    lol for real!! FAIL.. -_-

  78. jldstuff393
    • 2 years ago
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    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
    • 2 years ago
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    in his defense, tho, he's a stats guy, not calculus

  80. math456
    • 2 years ago
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    hmm but still. Stats is pretty much like math!

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