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Math Help - Limit

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    Limit

    Prove that \lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}=1.
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  2. #2
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    Quote Originally Posted by james_bond View Post
    Prove that \lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}=1.
    Use L'Hopital's rule

    \lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}= \lim_{x\rightarrow\infty}\frac {\frac{1}{1+x}}{\frac{1}{x}}= \lim_{x\rightarrow\infty}\frac {x}{x+1}=1
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