(a) Determine the Taylor polynomial T2(a) at 1 for the function f(x) = 2x-1 x+1 Show...

 

Transcribed Image Text:

(a) Determine the Taylor polynomial T2(a) at 1 for the function f(x) = 2x-1 x+1 Show that T2(a) approximates f(x) with an error of at most 0.0015 on the interval [1, 1.2]. (b) (i) Use the General Binomial Theorem to determine the first four terms of the Taylor series at 0 for the function f(x) = (1-3)-1/3 simplifying the coefficients of the terms. State the radius of convergence of this power series. (ii) Find the value of a that you need to substitute into the Taylor series from part (b)(i) to determine an approximate value for 41/3, and substitute it into the four terms from part (b)(i) to calculate an approximate value for 41/3. (c) Determine the interval of convergence of the power series (-1)" n1/3 3n (x-2)". n=1 (a) Determine the Taylor polynomial T2(a) at 1 for the function f(x) = 2x-1 x+1 Show that T2(a) approximates f(x) with an error of at most 0.0015 on the interval [1, 1.2]. (b) (i) Use the General Binomial Theorem to determine the first four terms of the Taylor series at 0 for the function f(x) = (1-3)-1/3 simplifying the coefficients of the terms. State the radius of convergence of this power series. (ii) Find the value of a that you need to substitute into the Taylor series from part (b)(i) to determine an approximate value for 41/3, and substitute it into the four terms from part (b)(i) to calculate an approximate value for 41/3. (c) Determine the interval of convergence of the power series (-1)" n1/3 3n (x-2)". n=1