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schmidtdancer

Use the information to evaluate the limits. I have a drawing attached.

  • one year ago
  • one year ago

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  1. schmidtdancer
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    |dw:1342983331687:dw|

    • one year ago
  2. schmidtdancer
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    @apoorvk Let me draw out the options from which I have to answer.

    • one year ago
  3. schmidtdancer
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    |dw:1342983428659:dw|

    • one year ago
  4. schmidtdancer
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    we can do one at a time .there are 4. but heres A^

    • one year ago
  5. schmidtdancer
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    @apoorvk ?

    • one year ago
  6. apoorvk
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    That's: lim [4 f(x)] ---> right? x ->c and [.] represents greatest integer function (GIF) - right?

    • one year ago
  7. schmidtdancer
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    Yes, and I think?

    • one year ago
  8. apoorvk
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    Ohkay... so.. that basically means I guess: |dw:1342983884987:dw| You have the value of that limit inside provided, you need to plug it in and proceed - understandable?

    • one year ago
  9. schmidtdancer
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    yeah

    • one year ago
  10. schmidtdancer
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    so would it be lim f(4)?

    • one year ago
  11. apoorvk
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    umm no, actually, that's 4 times the limits - \[[4 \times \lim \limits_{x\rightarrow c}^{}f(x) ]\]

    • one year ago
  12. schmidtdancer
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    Oh okay, how would I solve that?

    • one year ago
  13. apoorvk
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    and \(\lim \limits_{x\rightarrow c}^{}f(x) = 3/2\) is already given!

    • one year ago
  14. schmidtdancer
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    Ok

    • one year ago
  15. schmidtdancer
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    so what would we do divide 4?

    • one year ago
  16. schmidtdancer
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    im confsued.. what do we do

    • one year ago
  17. schmidtdancer
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    @apoorvk

    • one year ago
  18. apoorvk
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    Cool down your nerves - nothing to get confused about! :) (ain;t no monster :P lol) I just brought the whole limit expression inside the GIF brackets - we can do that since it will not affect the limit value). Then, since \(\large \lim\limits_{x \rightarrow t}k.f(x) = k.\lim\limits_{x \rightarrow t}f(x)\), for any function f(x) and constant k, I take the '4' out of the limit, and I end up with: \[[ 4.\lim\limits_{x \rightarrow c}f(x)]\]

    • one year ago
  19. schmidtdancer
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    lol. Ok so for a, we still have [4 lim f(x)] as x approaches c.. ok

    • one year ago
  20. apoorvk
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    Now it's given (in your first whiteboard drawing above) that \(\lim \limits_{x\rightarrow c}f(x) = 3/2\), I substitute that value into \([4\lim \limits_{x\rightarrow c}f(x)]\), an hence now I get: \[4 \times (3/2)\]

    • one year ago
  21. schmidtdancer
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    Yes, ok

    • one year ago
  22. schmidtdancer
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    So then a is: 6?

    • one year ago
  23. schmidtdancer
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    Can I write b now?

    • one year ago
  24. apoorvk
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    yes! sure

    • one year ago
  25. schmidtdancer
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    Kk im drawing now!

    • one year ago
  26. schmidtdancer
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    |dw:1342985761573:dw|

    • one year ago
  27. schmidtdancer
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    Is it just 2? I'm not sure

    • one year ago
  28. apoorvk
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    hey I need to make one thing sure - is that [.] for a step-up function or just general brackets?

    • one year ago
  29. apoorvk
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    if nothing's been stated, they're probably just general brackets~

    • one year ago
  30. schmidtdancer
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    what do you mean, sorry

    • one year ago
  31. schmidtdancer
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    Its lim [4f(x)] for a.

    • one year ago
  32. apoorvk
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    has anything been stated for those square brackets? If not am guessing they are just normal parenthesis, and not for GIF - in that case the second one would be 2 alright!

    • one year ago
  33. schmidtdancer
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    So a is still 6? and b is 2? lim [4f(x)] for a is exactly how it written

    • one year ago
  34. apoorvk
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    because:|dw:1342986392700:dw|

    • one year ago
  35. schmidtdancer
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    ok cool! so far i have a as 6, b as 2. Ill write c now

    • one year ago
  36. schmidtdancer
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    |dw:1342986644322:dw|

    • one year ago
  37. apoorvk
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    See, if [.] represents GIF, it should be mentioned, because in my education system, the rule is generally they would mention it if it is for a GIF - I am not sure about how's it stated in Us schools.

    • one year ago
  38. schmidtdancer
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    ok I wrote c. it says; lim[f(x)g(x)] as x-->c

    • one year ago
  39. apoorvk
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    Okay here you use the funda: |dw:1342986659285:dw|

    • one year ago
  40. schmidtdancer
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    Ok so would c be 3/4?

    • one year ago
  41. schmidtdancer
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    ?

    • one year ago
  42. apoorvk
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    yeah right!

    • one year ago
  43. schmidtdancer
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    yay! ok heres d

    • one year ago
  44. schmidtdancer
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    |dw:1342987062541:dw|

    • one year ago
  45. schmidtdancer
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    lim f(x)/g(x) as x--> c = ??

    • one year ago
  46. apoorvk
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    okay same way as the others - can you try this? You need to separate the two limits and then divide them.

    • one year ago
  47. schmidtdancer
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    Ok would it be 3?

    • one year ago
  48. schmidtdancer
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    |dw:1342987382978:dw|

    • one year ago
  49. apoorvk
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    Yeah right! good work!

    • one year ago
  50. schmidtdancer
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    thanks so much

    • one year ago
  51. apoorvk
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    no worries :]

    • one year ago
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