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How do you evaluate $\lim\limits_{x\to\infty}{\frac{1}{x}\ln(1+kx)}$? Thanks in advance.

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Try L'hospital rule. – Mickey Mouse Aug 30 '13 at 10:04
I'm sorry, why the downvote? I'd really like to know. – namehere Aug 30 '13 at 10:14
Maybe because you didn't show any effort to solve problem. Just saying (I didn't downvote) – Cortizol Aug 30 '13 at 10:51
up vote 3 down vote accepted

\begin{align*} \lim_{x\to\infty}{\frac{1}{x}\ln(1+kx)} &= \lim_{x\to\infty}\frac{\ln(1+kx)}{x}\\ &= \lim_{x\to\infty}\frac{\frac{k}{1+kx}}{1} && \text{l'Hospital's rule}\\ &= \lim_{x\to\infty}\frac{k}{1+kx}\\ &= \lim_{x\to\infty}\frac{k/x}{1/x+k}\\ &= \frac{0}{0+k}\\ &= \frac{0}{k}\\ &= 0\\ \end{align*}

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where $k\ne 0$. – kiss my armpit Aug 30 '13 at 10:57

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