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Improper Integrals and the Comparison Theorem

  1. Oct 10, 2007 #1
    Use the Comparisom Theorem to determine if

    [tex]f(x) = \int^{\infty}_{42} \frac{42+42^-x}{x}dx[/tex]

    is convergent or divergent.

    I compared it to [tex]g(x)=\int^{\infty}_{42} \frac{1}{x}dx[/tex]

    [tex]\int^{\infty}_{42} \frac{1}{x}dx = Lim_{t->\infty}\int^{t}_{42} \frac{1}{x}dx[/tex]

    Take the antiderivative, and the limit as t approaches infinity of ln(t)-ln(42) is infinity.

    So divergent.

    Looking for check. Thanks =P
     
    Last edited: Oct 10, 2007
  2. jcsd
  3. Oct 10, 2007 #2

    Gib Z

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    Homework Helper

    Yes that is correct.
     
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