Suppose g is a function which has continuous derivatives, and that g(8) = 3, g'(8) = 3, g'"(8) = −2, g"" (8) = 1. (a) What is the Taylor polynomial of degree 2 for g near 8? P₂(x) - P3(x) (b) What is the Taylor polynomial of degree 3 for g near 8? - (x−8)² + (x −8) 2 6 3 + 3(x − 8) − (x − 8)². = 3+3(x − 8) - (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(8.1). With P2, g(8.1)~≈ With P3, g(8.1) ≈

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A: Consider the provided question, The forward difference formula is given as,

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