I am stuck with applying limit at the following step, limit $$ \lim\limits_{s\to\infty}\log s. $$ Now I am unable to do anymore steps(I cant figure out how do I apply the limit and get a valid answer). Please help me out.
How to evaluate $\lim\limits_{s\to\infty}\log s$?
3
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limits
logarithms
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3There's no denominator. Anyway, what definition of $\ln$ are you using? If the integral definition, you're asking what the integral $\int_1^\infty \frac{\mathrm dt}{t}$ is... – 2011-10-31
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1I tried to guess which limit did you mean. It it right? – 2011-10-31
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1@akito - I'm not sure what you are asking. Do you want the limit of ln(s) as s becomes infinite? You have both s and S in your question. Are they the same thing, or is S dependent on s in some way? If they are the same, then it should be straightforward to show that ln(s) approaches infinity as s does. Otherwise, the question needs some clarifying. – 2011-10-31
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1@Akito: What is the base of your $log$? – 2011-10-31
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3@Hassan: does it matter here? – 2011-10-31
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0@J.M., yes it does, it should be bigger than 1. – 2013-06-08
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1@JMC, after excluding the bases $0$ and $1$, the logarithm remains sensible, no? – 2013-06-08
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0@J.M., for values smaller than 1 it tends to negative infinity (although you're right in the sense it is infinity as well). That was what I meant, sorry for the confusion. – 2013-06-08