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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.

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    There'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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    I tried to guess which limit did you mean. It it right?2011-10-31
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    @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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    @Akito: What is the base of your $log$?2011-10-31
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    @Hassan: does it matter here?2011-10-31
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    @J.M., yes it does, it should be bigger than 1.2013-06-08
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    @JMC, after excluding the bases $0$ and $1$, the logarithm remains sensible, no?2013-06-08
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    @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

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