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Math Help - Evaluate the limit

  1. #1
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    Evaluate the limit



    I know that i have to use L'Hos rule and to take a derevative, but I cant get it.
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    Quote Originally Posted by kashifzaidi View Post


    I know that i have to use L'Hos rule and to take a derevative, but I cant get it.
    Let y=\lim_{x\to\infty}\left(\frac{5x-1}{5x+3}\right)^{5x+2}

    Take the ln of both sides and see where that gets ya.
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  3. #3
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    Quote Originally Posted by kashifzaidi View Post


    I know that i have to use L'Hos rule and to take a derevative, but I cant get it.
    DO you have to use L'Hospital?

    Note that \frac{5x - 1}{5x + 3} = 1 - \frac{4}{5x + 3}.

    So \left(\frac{5x - 1}{5x + 3}\right)^{5x + 2} = \left(1 - \frac{4}{5x + 3}\right)^{5x + 2}


    The stuff inside the brackets \to 1 as x \to \infty.

    What does 1^{5x + 2} \to as x \to \infty?
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    Quote Originally Posted by kashifzaidi View Post


    I know that i have to use L'Hos rule and to take a derevative, but I cant get it.
    If you substitute u = 5x + 3 the limit can be written as \lim_{u \to + \infty} \left(1 - \frac{4}{u} \right)^{u - 1} and you can now use a well known limit involving our good friend e to easily get the answer.
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  5. #5
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    what is the other side ?
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    Quote Originally Posted by kashifzaidi View Post
    what is the other side ?
    y
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  7. #7
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    I did it...but I know that answer is not from the following: 0 , INFINITY or -INFINITY
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  8. #8
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    Quote Originally Posted by kashifzaidi View Post
    I did it...but I know that answer is not from the following: 0 , INFINITY or -INFINITY
    read this thread of related interest: http://www.mathhelpforum.com/math-he...te-limits.html

    Now read my first reply again.
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