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Math Help - solve a Lim +- 0

  1. #1
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    solve a Lim +- 0

    Lim +- 0 (1+2^(1/x))/(1-2^(1/x))
    Last edited by mr fantastic; November 18th 2009 at 02:53 PM. Reason: Included post title in main body of post
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by lyovadima View Post
    (1+2^(1/x))/(1-2^(1/x))
    Problem: Compute L=\lim_{x\to0^+}\frac{1+2^{\frac{1}{x}}}{1-2^{\frac{1}{x}}}

    Solution: Let z=\frac{1}{x} which transforms this into L=\lim_{x\to0^+}\frac{1+2^{\frac{1}{x}}}{1-2^{\frac{1}{x}}}\overbrace{\longmapsto}^{z=\frac{1  }{x}}\lim_{z\to\infty}\frac{1+2^z}{1-2^z}. Now, with a little manipulation L=\lim_{z\to\infty}\frac{\frac{1}{2^z}+1}{\frac{1}  {2^z}-1}. Clearly \frac{1}{2^z}\to0 so that L\to -1.
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    thanks it helps

    thanks it helps
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