(Taylor polynomials and Taylor series) Consider the function f(x) = (1-3x)/3 a. Provide the 4th degree...

 

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(Taylor polynomials and Taylor series) Consider the function f(x) = (1-3x)¹/3 a. Provide the 4th degree Taylor polynomial P4(x) of f(x) centered at 0. b. Provide the full Taylor series of f(x) centered at 0. To be precise, if the Taylor series has the form and then provide a general formula for the coefficient an n=0 c. Estimate the error of the 3rd-degree polynomial P3(0.01) from f(0.01). (Taylor polynomials and Taylor series) Consider the function f(x) = (1-3x)¹/3 a. Provide the 4th degree Taylor polynomial P4(x) of f(x) centered at 0. b. Provide the full Taylor series of f(x) centered at 0. To be precise, if the Taylor series has the form and then provide a general formula for the coefficient an n=0 c. Estimate the error of the 3rd-degree polynomial P3(0.01) from f(0.01).