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abannavong Group Title

help with AP calc hw plz!

  • 2 years ago
  • 2 years ago

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  1. Hero Group Title
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    Simply posting your actual question would be great

    • 2 years ago
  2. abannavong Group Title
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    im going to take a pic :3

    • 2 years ago
  3. abannavong Group Title
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    • 2 years ago
  4. abannavong Group Title
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    the limit is x->-1/2+

    • 2 years ago
  5. Hero Group Title
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    You've got like 5 questions circled. Which one is it?

    • 2 years ago
  6. abannavong Group Title
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    #38

    • 2 years ago
  7. campbell_st Group Title
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    perhaps factorising the numerator and denominator will allow you to cancel a common factor

    • 2 years ago
  8. abannavong Group Title
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    kk

    • 2 years ago
  9. satellite73 Group Title
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    limit as x goes to ???

    • 2 years ago
  10. Hero Group Title
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    -1/2

    • 2 years ago
  11. campbell_st Group Title
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    there is a common factor that is evident when you factorise numerator and denominator

    • 2 years ago
  12. satellite73 Group Title
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    then replace \(x\) by \(-\frac{1}{2}\) if you get a number, that is your answer any rational function is continuous on its domain so the limit and the value are the same

    • 2 years ago
  13. Hero Group Title
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    I think @campbell_st is right. You should try factoring the numerator and denominator first before plugging in x = -1/2

    • 2 years ago
  14. satellite73 Group Title
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    if you get \(\frac{2}{0}\) then you know you can factor both top and bottom as \((2x+1)(\text{something)}\)

    • 2 years ago
  15. satellite73 Group Title
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    i wouldn't do that, i would plug in first

    • 2 years ago
  16. campbell_st Group Title
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    the other thing about eliminating a common factor is that it makes the substitution calculation easier

    • 2 years ago
  17. satellite73 Group Title
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    if you get something other than \(\frac{0}{0}\) then that is the answer if you do get \(\frac{0}{0}\) then you know how to factor

    • 2 years ago
  18. Hero Group Title
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    If you plug in first, you're definitely going to get a denominator you won't like

    • 2 years ago
  19. satellite73 Group Title
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    @campbell_st i suck at factoring, so i like to know if i can factor first if i know i have a zero of a polynomial, i know already how to factor it that is why i would check first and not waste my time factoring, in case for example it does not factor over the integers

    • 2 years ago
  20. abannavong Group Title
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    so plugin -1/2 im kinda confused

    • 2 years ago
  21. Hero Group Title
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    Why waste your time trying to evaluate before factoring? Seems silly

    • 2 years ago
  22. campbell_st Group Title
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    lol... people get lost with squaring and substituting negative fractions... its really what works best you each of us

    • 2 years ago
  23. satellite73 Group Title
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    what i am trying to say is that if i replace \(x\) by \(-\frac{1}{2}\) i know it must factor as \((2x+1)\times (\text{whatever})\)

    • 2 years ago
  24. Zarkon Group Title
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    rational functions are continuous on their domain..if you plug in the value and you get a real number then that is the answer to the limit problem

    • 2 years ago
  25. satellite73 Group Title
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    because it tells me exactly how to factor otherwise i am doing the dance of what two numbers blah blah blah

    • 2 years ago
  26. campbell_st Group Title
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    here is the factorised version I hope... \[\lim_{x \rightarrow -\frac{1}{2}} \frac{(2x + 1)(3x -1)}{(2x + 1)(2x - 3)}\]

    • 2 years ago
  27. abannavong Group Title
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    kk

    • 2 years ago
  28. Hero Group Title
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    @satellite lost me. You're telling me that plugging in x = -1/2 tells you which two numbers you use to factor it?

    • 2 years ago
  29. satellite73 Group Title
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    @hero both @zarkon and i answered the question "why evaluate first" i think

    • 2 years ago
  30. satellite73 Group Title
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    yes, by the "factor theorem" if \(r\) is a root of a polynomial \(p(x)\) then we know \(p(x)=(x-r)q(x)\)

    • 2 years ago
  31. Hero Group Title
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    No, @zarkon said something I already knew. The problem is, if you plug in x = -1/2 in this case, you clearly get a zero denominator

    • 2 years ago
  32. Agent47 Group Title
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    This limit is begging for L'Hopital's Rule.....

    • 2 years ago
  33. satellite73 Group Title
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    it is not some miracle that each time you get \(\frac{0}{0}\) you can factor and cancel. it is precisely because of the factor theorem. you HAVE to be able to factor out the zeros

    • 2 years ago
  34. campbell_st Group Title
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    it doesn't need L'Hopital ... just factor to find it.... don't over think it

    • 2 years ago
  35. abannavong Group Title
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    im kinda confuzzled a bit :3

    • 2 years ago
  36. Agent47 Group Title
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    i can do lhopital in my head on this... but i guess it depends

    • 2 years ago
  37. Hero Group Title
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    That's because there's too many people trying to give their version of how to solve it.

    • 2 years ago
  38. satellite73 Group Title
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    what i am trying to say is this: you want the limit of a rational function as x approaches some number first thing you should do is check what you get when you evaluate the function at that number if you get a number back, that is your answer and you are done

    • 2 years ago
  39. campbell_st Group Title
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    looking at the type of questions you need to factorise to find the limit..

    • 2 years ago
  40. Agent47 Group Title
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    abanna, just listen to satellite, he's always right lol

    • 2 years ago
  41. Hero Group Title
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    I object to that statement^

    • 2 years ago
  42. satellite73 Group Title
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    if you get \(\frac{a}{0}\) where \(a\) is some non zero number, then there is no limit

    • 2 years ago
  43. campbell_st Group Title
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    @abannavong have a look above at my factorised version.. eliminate the common factor then substitute for your limit.

    • 2 years ago
  44. satellite73 Group Title
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    and if you get \(\frac{0}{0}\) then you know to factor and cancel AND you know how to factor

    • 2 years ago
  45. Hero Group Title
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    I see what you're saying now, @satellite. I usually do that part in my head first, but not on paper.

    • 2 years ago
  46. abannavong Group Title
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    oh ok

    • 2 years ago
  47. satellite73 Group Title
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    because for example, in this case we see that \(-\frac{1}{2}\) gives 0 that tells us that it MUST factor as \((2x+1)(\text{whatever})\) because \(2x+1\) has a zero at \(-\frac{1}{2}\)

    • 2 years ago
  48. campbell_st Group Title
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    @abannavong what level of maths is this...

    • 2 years ago
  49. satellite73 Group Title
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    and your job is then only to find the other factor, as @campbell_st wrote above

    • 2 years ago
  50. Agent47 Group Title
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    AB calculus, aka cal 1

    • 2 years ago
  51. abannavong Group Title
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    AP Calc :3

    • 2 years ago
  52. campbell_st Group Title
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    ok... so still high school... just I'm in australia...

    • 2 years ago
  53. abannavong Group Title
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    yeah in grade 12

    • 2 years ago
  54. campbell_st Group Title
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    thanks... I think you get 5/8 as the limit... good luck

    • 2 years ago
  55. abannavong Group Title
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    thank you @campbell_st

    • 2 years ago
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