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Questions and answers for a test covering a variety of things?

  1. Jun 21, 2011 #1
    im trying to study but i have um misplaced my textbook. (it ran away from me, after i neglected it whilst doing other assesments)

    so i would greatly appreciate just a couple questions with answers, (feel free to give me more though ;) )
    on any of these things (in order of priority)

    - squeeze theorem limits involving things that are not trigs
    - constant coeficients (complex, resonance, and nonhomogeneous and all these i think i want some working done because im not that good at these)
    - fourier series
    - trigonometry substitutions for integration
    - integral test (in a context or situation or something)
    - ratio test (in a context or situation or something)
    - radius of convergence (in a context or situation or something)
    - taylor series (harder ones for someone who has just been introduced to them maybe)
     
  2. jcsd
  3. Jun 21, 2011 #2

    Char. Limit

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    Gold Member

    Let's see... a few trig sub problems first, I suppose. Try these:

    [tex]\int x^2 \sqrt{9 - x^2} dx[/tex]

    [tex]\int \frac{1}{x \sqrt{x^2 - 1}}[/tex]

    [tex]\int \frac{1}{1 - x^4}[/tex]

    Hint: On the third problem, use partial fraction decomposition first.

    And a couple of integral test problems... are the following series convergent?

    [tex]\sum_{n=2}^\infty \frac{1}{n log_e(n)}[/tex]

    [tex]\sum_{n=1}^\infty \frac{n^3}{e^{n^2}}[/tex]

    And for what p is the following series convergent?

    [tex]\sum_{n=1}^\infty \frac{1}{n^p}[/tex]

    I'll think of questions for the other areas soon.
     
    Last edited: Jun 21, 2011
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