Mathematics I20815 marksTaylor's and Maclaurin's series
Find the Maclaurin series expansion of f(x) = sin x for all x.
Find the Maclaurin series expansion of $f(x) = \sin x$ for all x. [5]
The Maclaurin series of a function f(x) is the Taylor series expanded about x = 0, given by: $$f(x) = f(0) + f'(0)\cdot x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + \cdots + \frac{f^{(n)}(0)}{n!}x^n + \cdots$$ --- Let f(x) = sin x. We compute each derivative and evaluate at x = 0: n f^(n)(x...