State Taylor's theorem and hence obtain Macluarin's expansion in simplified form



State Taylor's theorem and hence obtain Macluarin's expansion in simplified form..

Answer / Sheetal Singh

Taylor's Theorem states that for a function f(x) that has n+1 continuous derivatives on an interval containing [a, x], the Taylor polynomial of degree n about a is given by:nP_n(x) = f(a) + (x-a)f'(a) + frac{(x-a)^2}{2!}f''(a) + ... + frac{(x-a)^n}{n!}f^{(n)}(a)nMaclaurin's expansion is the special case of Taylor's theorem when a = 0. So, Maclaurin's expansion is:nP_n(x) = f(0) + f'(0)x + frac{f''(0)x^2}{2!} + ... + frac{f^{(n)}(0)x^n}{n!}

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