Show that if f(x) = e cos x then and find f(0) and f(0). Differentiating the expression
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Show that if f(x) = ecos x then
and find f(0) and f´(0). Differentiating the expression for f´(x), obtain f"(x) in terms of f(x) and f´(x), and find f"(0). Repeating the process, obtain f(n)(0) for n = 3, 4, 5 and 6, and hence obtain the Maclaurin polynomial of degree 6 for f(x). Confirm your answer by obtaining the series using the Maclaurin expansions of ex and cos x.
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