Question

(10 points) Find the Maclaurin series for f(x) = 4" using the definition of a Maclaurin series. Justify all your steps.

Answer 1

o find the the maclaurin definition series of a for fin) = 4h, using madlauren series . Soln A Maclaurin finde series is given by Ě fk (0) xk K20 KI o from four for his file za flow, foly gion, flu) = 4 , flo): 40 = 2 f(x)= 4h log (4) flo) = loga fé 4" log(4). Log(4) f(0) = (boga32 f(n) = 4" (loge) f(0) = ( 109 413 (4(a)= 4 (loge, 4 (0) = (loga)

Therefore the geven as maclaurin series for find=an is 47. I 2° + 209(9) 24 Ty 034 (logy) + log 43 - 이 - ne 2 42 km Spony opetus, eyes, campfe on; qr - 2 + x logico) + 2² luge + 23 ( 1 2 3 4 2 ugast + - -