Question

Find the third MacLaurin polynomial for the function f(x) = e2x sin(3x)

Answer 1

we know that nth degree maclaurin polynomial of the function f(x) is given by,

Hence we can say that 3rd degree maclaurin polynomial is given by,

--------------------------------------------------------1)

we have,

Hence,

we have,

Hence,

we have,

Hence,

we have,

Hence,

we have,

Hence,

we have,

f(0) = 0, f'(0) = 3, f''(0) = 12 and f'''(0) = 9 put them in equation 1) we can say that third degree maclaurin polynomial is given by,