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Math Help - limit problem

  1. #1
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    limit problem

     lim_{x\to_\infty} (1+3x-3x^3+5x^5)

    Is there limit ?

    if yes , show the limit
    if not prove ...
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  2. #2
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    Quote Originally Posted by gilyos View Post
     lim_{x\to_\infty} (1+3x-3x^3+5x^5)

    Is there limit ?

    if yes , show the limit
    if not prove ...
    Hi

    The method consists in factoring out the maximum exponent

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

    The parenthesis has limit 5 at infinite therefore you can conclude
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  3. #3
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    This is the right problem

     lim_{x\to_\infty} (1+3x-3x^3+5x^5)^\frac{1}{x^2}
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  4. #4
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    In that case, put e^{ln} in front of the expression to bring down the exponent - then put the x^2 (which was part of the exponent) in the denominator while the really long term with all the x's is in the numerator and use L'Hopital's rule. Give it a shot.
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