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Thread: Trouble on Integral Test

  1. #1
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    Trouble on Integral Test

    Hi guys! I was doing a problem for my homework and I was doing great until the end. I got the integral correct and proved that the series converged but I'm having trouble understanding something. In the attached picture: I just need some explanation from at the point the limit is set up from t -> infinity and why they then set up another limit from s -> 0 and why for that latter portion they somehow got an e8. Thanks for all your help guys!

    Trouble on Integral Test-integraltestproblem.png
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  2. #2
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    Re: Trouble on Integral Test

    That is an s, not an 8. It is $e^s$.
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  3. #3
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    Re: Trouble on Integral Test

    If $\displaystyle \begin{align*} s = \frac{11}{t} \end{align*}$ then as $\displaystyle \begin{align*} t \to \infty , \, s \to 0 \end{align*}$...
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  4. #4
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    Re: Trouble on Integral Test

    omg, i legitimately couldn't tell. thanks so much!
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