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Math Help - L Hopital

  1. #1
    Junior Member
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    L Hopital

    Hi,

    For this problem, lim x->1 x^(1/(x-1))
    the answer is e, but i got the answer -1. could someone show me the steps. thanks.

    Oh yes, this problem also,
    lim x-> infinity xtan(1/x)

    so far, I did this: lim x-> infinity x(-1/x^2 sec^2(1/x)) + tan(1/x)(1)
    = lim x-> infinity -1/x sec^2(1/x) + tan(1/x)
    all i did was take derivative, but not sure what to do next or maybe i started off wrong...
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    You could try transforming into something more familiar.

    \lim_{x\rightarrow{1}}{x^{\frac{1}{x-1}}}

    Let t=\frac{1}{x-1}

    x=\frac{1}{t}+1

    \lim_{t\rightarrow{\infty}}\left(1+\frac{1}{t}\rig  ht)^{t}

    This is a famous limit which converges to e
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  3. #3
    Lord of certain Rings
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    Quote Originally Posted by ch2kb0x View Post
    Oh yes, this problem also,
    lim x-> infinity xtan(1/x)
    Applying L'Hopitals blindly will put you in a soup... You will never stop differentiating >_<
    Instead do a little manipulation first:
    Let x \rightarrow \frac1{u}
    \lim_{x\to \infty} x\tan\left(\frac1{x}\right) = \lim_{u\to 0} \frac{\tan(u)}{u}
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