How do you evaluate $\lim\limits_{x\to\infty}{\frac{1}{x}\ln(1+kx)}$? Thanks in advance.
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1$\begingroup$ Try L'hospital rule. $\endgroup$– Mickey MouseCommented Aug 30, 2013 at 10:04
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2$\begingroup$ I'm sorry, why the downvote? I'd really like to know. $\endgroup$– resghCommented Aug 30, 2013 at 10:14
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1$\begingroup$ Maybe because you didn't show any effort to solve problem. Just saying (I didn't downvote) $\endgroup$– CortizolCommented Aug 30, 2013 at 10:51
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1 Answer
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\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*}
answered Aug 30, 2013 at 10:22