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Math Help - Limit problem.

  1. #1
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    Limit problem.

    Hi, I´m having trouble solving this limit, without using the L´Hospital.

    limit_{x\to\infty}(\frac{2x+3}{2x+1})^x

    I tried dividing it into a sum and using Newtons binomial, but i arrived at


    limit_{x\to\infty}(\frac{4,481}{1+(1/2x)})^x

    which i am not able to solve. The answer should be e.
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  2. #2
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    Re: Limit problem.

    Hey HK47.

    Hint: Separate the fraction by using (2x+3)/(2x+1) = (2x + 1 + 2)/(2x+1) = 1 + 2/(2x+1) and look at the formula for e in terms of (1 + 1/n)^n.
    Thanks from HK47 and MarkFL
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  3. #3
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    Re: Limit problem.

    Thanks, expanded the binomial and discovered, that the constant doesnt contribute into the result.

    lim_x\to\infty{(1+\frac{1}{x+C})^x}=e

    Problem solved.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Limit problem.

    Try using the code:

    \lim_{x\to c}f(x)

    for your limits.
    Thanks from topsquark and HK47
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