Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus

HELP: Evaluate the limit: lim ((1/t)-(1/8))/ (t-8) = t->8

  • 9 months ago
  • 9 months ago

  • This Question is Closed
  1. alexwee123
    Best Response
    You've already chosen the best response.
    Medals 0

    is this the problem? |dw:1374780769038:dw|

    • 9 months ago
  2. kropot72
    Best Response
    You've already chosen the best response.
    Medals 2

    To find the limit consider values of t less than 8 (t approaches 8 from below) and values of t greater than 8 (t approaches 8 from above) and construct a table for the value of f(t) using the following values of t: 7.9, 7.95, 7.99, 8, 8.01, 8.05, 8.1 Although f(8) is undefined, you can still find a value for the limit.

    • 9 months ago
  3. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    can you show me?

    • 9 months ago
  4. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i've tried every way but i've gotten it incorrect a couple of times..

    • 9 months ago
  5. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @kropot72

    • 9 months ago
  6. kropot72
    Best Response
    You've already chosen the best response.
    Medals 2

    To start your table by finding the value of f(7.9) just plug 7.9 into the expression for f(t) \[f(7.9)=\frac{\frac{1}{7.9}-\frac{1}{8}}{7.9-8}=you\ can\ calculate\] Then find f(7.95), f(7.99), f(8.01), f(8.05) and f(8.1). The limit will become clear when you have finished your table.

    • 9 months ago
  7. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    is there another way to do this?

    • 9 months ago
  8. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    besides approaching it to the closest number?

    • 9 months ago
  9. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    not the table method.

    • 9 months ago
  10. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @kropot72

    • 9 months ago
  11. kropot72
    Best Response
    You've already chosen the best response.
    Medals 2

    There is a quick method. \[\frac{\frac{1}{t}-\frac{1}{8}}{t-8}=\frac{8-t}{8t}\times\frac{-1}{8-t}=\frac{-1}{8t}\] When you plug the value t=8 into this expression you get a value for the limit. This method is not as reliable as the table method, the reason being that it does not check that the limit is aproached to the same value from above and below the limit.

    • 9 months ago
  12. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @kropot why did you multiply it by -1?

    • 8 months ago
  13. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @dumbcow could u be able to help me with this problem?

    • 8 months ago
  14. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @Loser66 i got 8-t/8t but then after i'm not sure how they got -1/8t

    • 8 months ago
  15. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    you were typing? lol

    • 8 months ago
  16. Loser66
    Best Response
    You've already chosen the best response.
    Medals 0

    kropot72 gave you the right logic , just plug t =8 to get -1/64, done

    • 8 months ago
  17. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i know, but i understand up to here: 8-(8)/8t... but then if i plug in 8 into this.... then i get 0/64 which is not right..... because im suppose to get a -1 on top/8(t)

    • 8 months ago
  18. Loser66
    Best Response
    You've already chosen the best response.
    Medals 0

    re read the stuff, you missed something, it 's not that.

    • 8 months ago
  19. dumbcow
    Best Response
    You've already chosen the best response.
    Medals 0

    another option is l'hopitals rule since you get 0/0 when evaluating limit differentiate top/bottom separately then reevaluate you should get lim = -1/64

    • 8 months ago
  20. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i know, my question is why did he multiply -1/8-t ?

    • 8 months ago
  21. Loser66
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, dumbcow 's solution is ok, too. but kropot 72 's solution is ok, too. Yours is wrong, hehe

    • 8 months ago
  22. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375031598300:dw|

    • 8 months ago
  23. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    does that clarify it?

    • 8 months ago
  24. Loser66
    Best Response
    You've already chosen the best response.
    Medals 0

    yup, bravo @asnaseer

    • 8 months ago
  25. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @asnaseer yes:) just need to know why we multiply -1/8-t?

    • 8 months ago
  26. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @Loser66 not helping. bye

    • 8 months ago
  27. Loser66
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, just because you tag me, I leave now, thanks for sending me away

    • 8 months ago
  28. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    @kropot72 made use of the fact that:\[\frac{1}{t-8}=\frac{-1}{8-t}\]

    • 8 months ago
  29. dumbcow
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathcalculus , its because the denominator was "t-8" the rule when dividing is multiply by reciprocal ... which turns it into 1/t-8 then they factored out a neg

    • 8 months ago
  30. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    ooooh okay. thank you so much @dumbcow

    • 8 months ago
  31. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    @asnaseer thank you!

    • 8 months ago
  32. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    yw :)

    • 8 months ago
  33. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    hold oni just multiplied 8-t/8t by 1/t-8 and i got this: 8-t/8t^2-64 @asnaseer

    • 8 months ago
  34. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    im not sure what to do after:?

    • 8 months ago
  35. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375032333583:dw|

    • 8 months ago
  36. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    the terms with (8-t) cancel out

    • 8 months ago
  37. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    remember:\[t-8=-(8-t)\]therefore:\[\frac{1}{t-8}=\frac{1}{-(8-t)}=\frac{-1}{8-t}\]

    • 8 months ago
  38. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah but i can't see that when im doing this problem alone.. im thinking i multiply across.. is that possible?

    • 8 months ago
  39. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    or cross multiply*

    • 8 months ago
  40. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    in order to evaluate the limit you need to either simplify the fraction (which is what we did), or use l'Hopitals rule (as suggested by dumbcow)

    • 8 months ago
  41. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    but can we or no?

    • 8 months ago
  42. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i have not used the l hospitals rule yet.

    • 8 months ago
  43. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    if you use the first method, then you need to cancel out the common factors in the fraction, i.e. cancel out the (8-t) from the numerator and the denominator

    • 8 months ago
  44. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i see that

    • 8 months ago
  45. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    if you don't cancel these out and just multiply across then you will end up with a fraction that goes to zero divided by zero as t approaches 8

    • 8 months ago
  46. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i know, but all i see is that i can cross multiply but how do you know that the t-8 needed to be factored?

    • 8 months ago
  47. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    it was just a /hunch/ - it was a good candidate to try and cancel out as it tends to zero as t approaches 8.

    • 8 months ago
  48. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    and we want to avoid zeros (especially in the denominators) when evaluating limits

    • 8 months ago
  49. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    e.g. find the limit as t tends to 2 of:\[\frac{t^2-2t}{2t-4}\]

    • 8 months ago
  50. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    if you just stick t=2 into this, you will get 0/0 which is undefined

    • 8 months ago
  51. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    so first we try to factorise it and see if we get anything interesting

    • 8 months ago
  52. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{t^2-2t}{2t-4}=\frac{t(t-2)}{2(t-2)}\]

    • 8 months ago
  53. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    now we notice a (t-2) can be cancelled out

    • 8 months ago
  54. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{t^2-2t}{2t-4}=\frac{t\cancel{(t-2)}}{2\cancel{(t-2)}}=\frac{t}{2}\]

    • 8 months ago
  55. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    now we can evaluate the limit as t->2

    • 8 months ago
  56. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    hope that makes sense?

    • 8 months ago
  57. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so i did this now: 8-t/8t * 1/- (8-t)

    • 8 months ago
  58. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i cancel the 8-t... but what about the negative sign outside of it???

    • 8 months ago
  59. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    im left with 1/8t

    • 8 months ago
  60. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    the negative sign can just be moved up to the 1

    • 8 months ago
  61. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    but not -1??

    • 8 months ago
  62. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    why??

    • 8 months ago
  63. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375033388098:dw|

    • 8 months ago
  64. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    all 3 forms are equivalent

    • 8 months ago
  65. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    i need rules, not simply "oh because we can." "just guessing" "that works"

    • 8 months ago
  66. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    oay i understand that

    • 8 months ago
  67. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    the rules here are to look for common factors that can be cancelled out

    • 8 months ago
  68. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    so when i asked u if we can multiply across, can we or not?

    • 8 months ago
  69. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    in later classes you will be given limits where the fractions cannot be simplified. that is where you may be introduced to l'hopitals method.

    • 8 months ago
  70. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    you CAN multiply across but it won't simplify the fraction. why wouldn't you want to cancel out the common terms BEFORE multiplying?

    • 8 months ago
  71. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    e.g.: |dw:1375033624859:dw|

    • 8 months ago
  72. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    or: |dw:1375033674334:dw|

    • 8 months ago
  73. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    okay from here:8-t/8t^2-64t

    • 8 months ago
  74. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    lead to the same simplification

    • 8 months ago
  75. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    so how do i do this after?

    • 8 months ago
  76. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    yes - then you will have to re-factorise the denominator to cancel out the (8-t)

    • 8 months ago
  77. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375033741276:dw|

    • 8 months ago
  78. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    okay i understand.

    • 8 months ago
  79. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    great! :)

    • 8 months ago
  80. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    now when i cancel... and the negative sign is all alone. can i replace it by a negative 1 since -1/1 or 1/-1 is the same??

    • 8 months ago
  81. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    yes :)

    • 8 months ago
  82. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks! =]

    • 8 months ago
  83. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    yw :)

    • 8 months ago
  84. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    can we go over another problem so i can feel more confident on it? @asneer

    • 8 months ago
  85. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    sure - just post it as a new question please

    • 8 months ago
  86. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    • 8 months ago
    1 Attachment
  87. mathcalculus
    Best Response
    You've already chosen the best response.
    Medals 0

    k

    • 8 months ago
  88. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 1

    <<<--- please post as a new question in the list on the left it helps others learn as well :)

    • 8 months ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.