Find the third order Taylor polynomial P3(x), an approximation of f(x) = 1/x½ about x0 = 1.
Choose from the following options:
P3(x) = 1 + (x-1) + (x-1)2 + (x-1)3
P3(x) = 1 - (x-1) + (x-1)2 - (x-1)3
P3(x) = 1 + 3/2(x-1) + 3/8(x-1)2 - 1/16(x-1)3
P3(x) = 1 + 3/2(x-1) + 5/8(x-1)2 - 7/16(x-1)3
P3(x) = 1 + 2(x-1) + 8(x-1)2 + 16(x-1)3
P3(x) = 1 + 1/2(x-1) - 1/8(x-1)2 + 1/16(x-1)3
P3(x) = - 1 + 1/2(x-1) - 3/8(x-1)2 + 5/16(x-1)3
P3(x) = 1 - 2(x-1) + 3(x-1)2 - 4(x-1)3
P3(x) = 1 + 2(x-1) - 8(x-1)2 + 16(x-1)3
P3(x) = 1 - 1/2(x-1) + 3/8(x-1)2 - 5/16(x-1)3
Please respond in full explanation so i can understand the steps! thanks so much in advance!