1. (i) Given that f(x) = 1n (1 + 2 sin x), find f(0), f'(0), f''(0), f'''(0). Hence write down the first three non-zero terms in the Maclaurin series for f(x). [ 7 ]
(ii) The first two non-zero terms in the Maclaurin series for f(x) are equal to the first two non-zero terms in the series expansion of e^ax sin nx. Using appropriate expansion from the List of Formulae (MF15), find the constants a and n. Hence find the third non-zero term of the seri...