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Textbook not clear please help explain this question(s)

  1. Apr 6, 2008 #1
    [SOLVED] Textbook not clear.... please help explain this question(s)...

    Question 1.

    1. The problem statement, all variables and given/known data

    State whether the limit exists for (Limit as x aproaches infinity ==> (n+1)/(n+1)

    and give the value of it if it does exist. Graph the first 5 terms of each sequence.


    3. The attempt at a solution


    if you use any number for "n", numerator divided by denominator would equal 1.


    Question 2:



    1. The problem statement, all variables and given/known data
    The sequence a1, a2, a3 ..... has the following possible nth terms. For the case given below try various large values for n and guess the limit. Confirm that guess by manipulating the general term an.

    a(n) = (n+1) / (n^2+1)





    I'm taking a intro Calc class, so this is probably easy stuff for you guys, that's why I lumped both questions into one thread. Anhow, I'm not looking for an answer since it's in my book, I just want to know what the question is asking for.
     
  2. jcsd
  3. Apr 6, 2008 #2
    and.... where's that thread that explains how to use syntax.


    edit: nm, I just found it....latex not syntax lol
     
  4. Apr 6, 2008 #3

    Dick

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    So what's your question? Did you follow the suggestion and substitute various values of n? What's your guess of the limit?
     
  5. Apr 6, 2008 #4
    question 1: limit equals 1?
     
  6. Apr 6, 2008 #5
    question 2:


    answer:

    an = n + 1 / n^2 + 1

    possible answers: 11/101, 101/10001, 1001/1000001 appears to have limit of zero?


    but how does it have limit of zero?
     
  7. Apr 6, 2008 #6

    Dick

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    Yep. Can you prove it? Divide numerator and denominator by n.
     
  8. Apr 6, 2008 #7

    Dick

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    Same answer, yes. Can you prove it? Divide numerator and denominator by n^2.
     
  9. Apr 6, 2008 #8
    oh wait....question 2's answer is from the book, not mine.

    I attempted it the same way..............except


    what I don't understand is how it has a limit of zero?
     
  10. Apr 6, 2008 #9

    Dick

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    Ok, divide numerator and denominator of 2) by n^2. This gives you (1/n+1/n^2)/(1+1/n^2), right? What's the limit of 1/n and 1/n^2?
     
  11. Apr 6, 2008 #10
    wait....

    the question is (n + 1) / (n^2 +1)

    so divide num/denom by n^2 it should be


    (n/n^2) + (1/n^2) / (n^2/n^2) + (1/n^2) right?


    then it goes

    (1/n) + (1/n^2) / 1 + (1/n^2)

    then it goes, which is the step I don't understand...


    (0+0) / (1 + 0) = 0/1 = 0


    where are all these zero's coming from?
     
  12. Apr 6, 2008 #11

    Dick

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    The limit of 1/n as n goes to infinity is zero. Likewise for 1/n^2. The numerator is 1 and the denominator gets larger and larger.
     
  13. Apr 6, 2008 #12
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