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Math Help - taylors theorem

  1. #1
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    taylors theorem

    Maclaurin's theorem is a specific form of Taylor's theorem, or a Taylor's power series expansion, where c = 0 and is a series expansion of a function about zero.
    What does c mean here? Is it the constant of integration?
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  2. #2
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    Quote Originally Posted by linyen416 View Post
    Maclaurin's theorem is a specific form of Taylor's theorem, or a Taylor's power series expansion, where c = 0 and is a series expansion of a function about zero.
    What does c mean here? Is it the constant of integration?
    A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function about a point x=c is given by:

    f(x) = f(c) + f'(c)(x-c) + \frac{f''(c)}{2!} (x-c)^2 + \frac{f'''(c)}{3!} (x-c)^3 + \frac{f''''(c)}{4!}(x-c)^4 + ... + \frac{f^{(n)}(c)}{n!} (x-c)^n+...

    A Maclaurin series is a Taylor series expansion of a function about c=0 which is given by:

    f(x) = f(0) + f'(0)x + \frac{f''(0)}{2!} x^2 + \frac{f'''(0)}{3!} x^3 + \frac{f''''(0)}{4!} x^4 + ... + \frac{f^{(n)}(0)}{n!} x^n+...
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