Question: Find the third order Taylor polynomial P 3 ( x ), an approximation of f ( x ) = 1/ x about x 0 =

Find the third order Taylor polynomialP3(x), an approximation off(x) = 1/xaboutx0= 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!

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