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Math Help - LImits at infinity help: Indeterminate forms

  1. #1
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    Unhappy LImits at infinity help: Indeterminate forms

    Help with these: Find the limit if it exists
    Last edited by ^_^Engineer_Adam^_^; March 9th 2007 at 08:14 PM.
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  2. #2
    Junior Member frenzy's Avatar
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    do you know L'Hopital's rule?
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  3. #3
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  4. #4
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    Number 3 has an answer similar to this:




    Question: how did (2x-1)/(2sqrt(x^2-x)) became 1?
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  5. #5
    Junior Member frenzy's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Number 3 has an answer similar to this:




    Question: how did (2x-1)/(2sqrt(x^2-x)) became 1?
    for x>0

    sqrt(x^2-x)=x*sqrt(1-1/x)

    now simplify (2x-1)/(2sqrt(x^2-x)) and take the limit.
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  6. #6
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    Is The answer of number 1 e^1? and thanks
    no need for 2 & 3 ive already answered it
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  7. #7
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Is The answer of number 1 e^1? and thanks
    no need for 2 & 3 ive already answered it

    No (1) diverges.

    Take logs and then consider the limit of x^2 ln(1+1/(2x)) using L'Hopital's rule.

    RonL
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  8. #8
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    The answer of no. 1 is e^(-4)? Isnt it?
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The answer of no. 1 is e^(-4)? Isnt it?
    (1+1/(2*10))^(10^2) ~= 131

    (1+1/(2*100))^(100^2) ~= 4.6 10^21

    L'Hopital says it diverges, and numerical experiment supports that.

    RonL
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