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schmidtdancer

  • 3 years ago

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

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  1. schmidtdancer
    • 3 years ago
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    |dw:1342983331687:dw|

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

  3. schmidtdancer
    • 3 years ago
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    |dw:1342983428659:dw|

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

  5. schmidtdancer
    • 3 years ago
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    @apoorvk ?

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

  7. schmidtdancer
    • 3 years ago
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    Yes, and I think?

  8. apoorvk
    • 3 years ago
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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?

  9. schmidtdancer
    • 3 years ago
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    yeah

  10. schmidtdancer
    • 3 years ago
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    so would it be lim f(4)?

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

  12. schmidtdancer
    • 3 years ago
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    Oh okay, how would I solve that?

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

  14. schmidtdancer
    • 3 years ago
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    Ok

  15. schmidtdancer
    • 3 years ago
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    so what would we do divide 4?

  16. schmidtdancer
    • 3 years ago
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    im confsued.. what do we do

  17. schmidtdancer
    • 3 years ago
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    @apoorvk

  18. apoorvk
    • 3 years ago
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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: \[[ 4.\lim\limits_{x \rightarrow c}f(x)]\]

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

  20. apoorvk
    • 3 years ago
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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: \[4 \times (3/2)\]

  21. schmidtdancer
    • 3 years ago
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    Yes, ok

  22. schmidtdancer
    • 3 years ago
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    So then a is: 6?

  23. schmidtdancer
    • 3 years ago
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    Can I write b now?

  24. apoorvk
    • 3 years ago
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    yes! sure

  25. schmidtdancer
    • 3 years ago
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    Kk im drawing now!

  26. schmidtdancer
    • 3 years ago
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    |dw:1342985761573:dw|

  27. schmidtdancer
    • 3 years ago
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    Is it just 2? I'm not sure

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

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

  30. schmidtdancer
    • 3 years ago
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    what do you mean, sorry

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

  32. apoorvk
    • 3 years ago
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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!

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

  34. apoorvk
    • 3 years ago
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    because:|dw:1342986392700:dw|

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

  36. schmidtdancer
    • 3 years ago
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    |dw:1342986644322:dw|

  37. apoorvk
    • 3 years ago
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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.

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

  39. apoorvk
    • 3 years ago
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    Okay here you use the funda: |dw:1342986659285:dw|

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

  41. schmidtdancer
    • 3 years ago
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    ?

  42. apoorvk
    • 3 years ago
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    yeah right!

  43. schmidtdancer
    • 3 years ago
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    yay! ok heres d

  44. schmidtdancer
    • 3 years ago
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    |dw:1342987062541:dw|

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

  46. apoorvk
    • 3 years ago
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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.

  47. schmidtdancer
    • 3 years ago
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    Ok would it be 3?

  48. schmidtdancer
    • 3 years ago
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    |dw:1342987382978:dw|

  49. apoorvk
    • 3 years ago
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    Yeah right! good work!

  50. schmidtdancer
    • 3 years ago
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    thanks so much

  51. apoorvk
    • 3 years ago
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    no worries :]

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