Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question
1  
Try L'hospital rule. –  Mickey Mouse Aug 30 '13 at 10:04
2  
I'm sorry, why the downvote? I'd really like to know. –  namehere Aug 30 '13 at 10:14
1  
Maybe because you didn't show any effort to solve problem. Just saying (I didn't downvote) –  Cortizol Aug 30 '13 at 10:51
add comment

1 Answer 1

up vote 4 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*}

share|improve this answer
    
where $k\ne 0$. –  Please don't touch Aug 30 '13 at 10:57
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.