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Thread: solve limit with high powers

  1. #1
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    solve limit with high powers

    How do I calculate this limit?
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  2. #2
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    Using L'Hospital's Rule... many times...
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    It is the only way?
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    No, you could also expand everything, then divide top and bottom by the highest power of $\displaystyle x$.
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    The limit will be $\displaystyle \left(\frac{3}{2}\right)^{20}$.

    To see that notice that $\displaystyle (3x-1)^{20}=3^{20}x^{20}\left(1-\frac{1}{3x}\right)^{20}$.
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  6. #6
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    I did it in a different, longer way.

    (3x-1)^20 = ((3x-1))^10.

    This way I've put the power of ten outside the whole expression and after a couple of lines ended up with (9/4)^10.

    Your way is much shorter, I should notice such things in the future, thanks.
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