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Math Help - Help plz!

  1. #1
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    Help plz!

    It's again prbls w/ l'Hospital rule.
    omg, my calc prof. assigned like 50 prbls but i had to study for my other finals. these are due today at 9. plz help.

    1) lim(1+e^x)^(1/x)
    x->infinity
    "infinity^0" type?
    =e^lim (1/x)ln(1+e^x)

    2)lim (1+(3/x^2)^x
    x->infinity
    "1^infinity" type
    =e^ilm x ln(1+3/x^2)

    3) lim x sin x/ (1-cos x)
    this one i have no idea what to do.

    plz help me so that i can just get some sleep. it's already 4 in the morning.
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  2. #2
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    Quote Originally Posted by katieeej View Post
    It's again prbls w/ l'Hospital rule.
    omg, my calc prof. assigned like 50 prbls but i had to study for my other finals. these are due today at 9. plz help.

    1) lim(1+e^x)^(1/x)
    x->infinity
    "infinity^0" type?
    =e^lim (1/x)ln(1+e^x)

    2)lim (1+(3/x^2)^x
    x->infinity
    "1^infinity" type
    =e^ilm x ln(1+3/x^2)

    3) lim x sin x/ (1-cos x)
    this one i have no idea what to do.

    plz help me so that i can just get some sleep. it's already 4 in the morning.
    3) has already been done here: http://www.mathhelpforum.com/math-he...le-urgent.html Please pay closer attention so that you don't post the same questions more than once.
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  3. #3
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    Quote Originally Posted by katieeej View Post
    It's again prbls w/ l'Hospital rule.
    omg, my calc prof. assigned like 50 prbls but i had to study for my other finals. these are due today at 9. plz help.

    1) lim(1+e^x)^(1/x)
    x->infinity
    "infinity^0" type?
    =e^lim (1/x)ln(1+e^x)

    2)lim (1+(3/x^2)^x
    x->infinity
    "1^infinity" type
    =e^ilm x ln(1+3/x^2)

    3) lim x sin x/ (1-cos x)
    this one i have no idea what to do.

    plz help me so that i can just get some sleep. it's already 4 in the morning.
    I will get you started with 1). 2) is similar and easier.

    \lim_{x \rightarrow +\infty} \left( 1 + e^x \right)^{\frac{1}{x}} = \lim_{x \rightarrow +\infty} \exp \left( \frac{\ln (1 + e^x)}{x}\right) = \exp \left( \lim_{x \rightarrow +\infty} \frac{\ln (1 + e^x)}{x} \right).

    (The justification is left for you to give).

    So you need to consider the limit \lim_{x \rightarrow +\infty} \frac{\ln (1 + e^x)}{x}. Use l'Hopital's Rule twice.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    I will get you started with 1). 2) is similar and easier.

    \lim_{x \rightarrow +\infty} \left( 1 + e^x \right)^{\frac{1}{x}} = \lim_{x \rightarrow +\infty} \exp \left( \frac{\ln (1 + e^x)}{x}\right) = \exp \left( \lim_{x \rightarrow +\infty} \frac{\ln (1 + e^x)}{x} \right).

    (The justification is left for you to give).

    So you need to consider the limit \lim_{x \rightarrow +\infty} \frac{\ln (1 + e^x)}{x}. Use l'Hopital's Rule twice.
    i'm so sorry but can you give me some more details?
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  5. #5
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    Quote Originally Posted by katieeej View Post
    i'm so sorry but can you give me some more details?
    What don't you follow?


    Edit: Note: (1 + e^x)^{\frac{1}{x}} = e^{\ln (1 + e^x)^{\frac{1}{x}}} = e^{\frac{1}{x}\ln (1 + e^x)}
    Last edited by mr fantastic; March 13th 2009 at 04:00 AM.
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