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Thread: another comparison thereom problem

  1. November 1st 2009, 12:04 PM #1
    calcbeg
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    another comparison thereom problem

    Hi

    I am suppose to use the comparison thereom to determine if the following integral is convergent or divergent

    integral sign (S) a= e and b= infinity (2010 + cos 2011 x)/ 2009x dx

    these numbers are huge and I don't know where to start - especially with a cos in the middle of it.

    Help!

    Calculus beginner
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  2. November 2nd 2009, 03:37 PM #2
    Media_Man
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    I=\int_0^\infty \frac{2010+\cos(2011x)}{2009x}dx

    The range for cosine is [-1,1], so the numerator N\in[2009,2011]. The entire fraction f(x)\in[\frac{1.001}x,\frac1x].

    So, since f(x)>\frac{1.001}x, I>\int_0^\infty\frac{1.001}{x}dx. Can you get it from here?
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