Suppose f(t) can be written in a Taylor series representation centered at a number a as...
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Suppose f(t) can be written in a Taylor series representation centered at a number a as f"" (a) 6 (ta)³ + Suppose h> 0 below. a. Substitute t = x + h and a = x above and write the result. b. Substitute t = x  h and a = x above and write the result. Combine the information from parts a and b to show that f'(a) can be written in the form f" (a) = N₁(h) + K₂h² + K₂h¹ + ... where K₂, K4, etc. are independent of h, and give an explicit formula for N₁ (h). d. Explain why N₁ (h) is an 0(h²) approximation of f'(a). Do you recognize N₁ (h)? Use N₁ (h) and N₁ to create an 0 (h4) approximation N₂ (h) of f'(a). C. 1 f(t) = f(a) + ƒ'(a)(t − a) +=ƒ''(a)(t − a)² + = e.
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