Find the third Taylor polynomial P₁(x) for the function f(x)=(x-1) Inx about xp = 1. a. Use P, (0.5) to approximate /(0.5). Find an upper bound for error 1/(0.5) - P, (0.5) using the error formula, and compare it to the actual error. b. C. d. Find a bound for the error f(x) - P(x) in using P(x) to approximate f(x) on the interval 10.5. 1.51. Approximate fs fix) dx using P,(x) dx. Find an upper bound for the error in (c) using as IR.(x) dx), and compare the bound to the actual error.

Use the Newton forward difference formula to construct interpolating polynomials of degree three for the following data. Approximate f(-0.3) f(-0.75) = -0.0718, f(-0.5) = -0.0247, f(-0.25) = 0.3349, f(0) = 1.1010

Find the nth Maclaurin polynomial for the function. f(x) = tan x, n = 3 P3(x) =

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