Find the Taylor polynomial of order 3 generated by f at a. f(x) = x², a = 2 A. P3(x) = 1 +8(x- 2) + 24(x- 2)2 + 64(x– 2)3 O B. P3(x) = 1 + 4(x - 2) + 6(x- 2)² +8(x- 2)³ O c. P3(x) = 4 + 4(x- 2) + 6(x- 2)² + 8(x- 2)3 D. P3(x) = 4 + 4(x- 2) + (x- 2)2

Q: ose P(x) is a polynomial satisfying - P(5) = - 5 - P'(5) = - 305 - P''(5) = – 156 - P(3) (5) = - 414…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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Q: Find the Taylor polynomial of order 3 generated by fat a. f(x) = x2 +x+1, a=2 O A. P3(x) =7+5(x- 2)…

A: f(x)=x2+x+1f(2)=4+2+1 =7f'(x)=2x+1f'(2)=4+1 =5f''(x)=2f''(2)=2f'''(2)=0

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A: To find: the definition of the remainder Rn(x) in a Taylor polynomial.

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A: Option A is correct .

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