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Math Help - Approximating Integrals

  1. #1
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    Approximating Integrals

    The question asks to approximate

    (-1 +cosx)/x^2

    to the nearest 0.01

    Just wondering, do I take the function to the fourth derivative etc, or is there some other way to solve this? Because that way is becoming too tedious and not really yielding the correct answer.

    Thanks!
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  2. #2
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    Re: Approximating Integrals

    Quote Originally Posted by bhaktir View Post
    The question asks to approximate

    (-1 +cosx)/x^2

    to the nearest 0.01

    Just wondering, do I take the function to the fourth derivative etc, or is there some other way to solve this? Because that way is becoming too tedious and not really yielding the correct answer.

    Thanks!
    limits of integration?

    use of the series representation for cos(x), maybe ?
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  3. #3
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    Re: Approximating Integrals

    "to the nearest 0.01"

    ^ Does this mean I go up to the (-1/3) value or further? Dumb question, I know, but could you explain what "to the nearest 0.01" means in this context?

    Thanks for the power series representation tip!
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  4. #4
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    Re: Approximating Integrals

    |error| < 0.01
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  5. #5
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    Re: Approximating Integrals

    Still confused. See, when I start entering n values (starting from n=0) into the power series representation, I get: 0, -1/3, 1/30... etc.

    Now, to approximate the function to within 0.01, which n value do I need to stop at?
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  6. #6
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    Re: Approximating Integrals

    Quote Originally Posted by bhaktir View Post
    Still confused. See, when I start entering n values (starting from n=0) into the power series representation, I get: 0, -1/3, 1/30... etc.

    Now, to approximate the function to within 0.01, which n value do I need to stop at?
    research the error bound for an alternating series
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  7. #7
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    Re: Approximating Integrals

    Kk. Thanks!
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