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Answer all parts of the question and provide work pls. Will provide a positive feedback score if completed : )
17. (20 points) Answer the following questions. You may use the results in the consequent problems as necessary: (a) Use the
(b) The Taylor series centered at x = 0 for arctan(s) given in part (a) converges to arctan(x) on its interval of convergence
(e) Find the radius and interval of convergence for the Taylor series centered at x = 2 for g(x) found in part (6).
(d) Write the 8th degree Taylor polynomial expansion centered at x = 2 for g(x) and evaluate g® (2).
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Answer #1

ca) f(x) 1+x? - (محمد-)- 74x2 2² = y Consider n for lyl</ Σ 8 - ha 1-y - This gives } (-2²) Ž-D hco - 2n 2 1xl<1 14x² for t31 2 = (x) و (.-a) دات کے 2. * : ** (2+1) To find radius of convergence, will find ع لا (c) 25+ 2 lim Unt! where :-(-) : ا Un2-42 g(x) Î (-1 (x-2) (9) 11 ho ,20+ (2140) 3 2 (2-2) (x-2) 3² 7 => 962), (0-2) +(40) 3.5 3 33.3 Ĉ en (x-a, Consider g(x)

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