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Find the Taylor polynomial PA(a) centered at a = 1 for the function f(x) = 11 x. a) Ol1 + 11 (2 - 1)+- 11 2 8 (2 - 1) + 11 16 (2 - 1)3 55 + 128 (2 - 1)4 b) Ol1 + 11 (x - 1) 11 (a - 1) + 33 2 (x - 1)3 165 4 8 16 (2 - 1)4 11 c) O l1 + 2 (2 - 1) 11 11 55 8 (z - 1)2 + 16 (2 - 1)3 128 (x - 1)4 d) Ol1 + (z - 1) 11 55 16 (2 - 1)2 + 35 (2 - 1)3 32 (z - 1)4 e) O 11 - 11 2 (2 - 1) 11 8 (z - 1)2 11 16 (2 - 1)3 55 128 (x - 1)4\fFind the Taylor polynomial PA(a) centered at a = 0 for the function f(x) = x - 3 cos(x). a) 03-T 4 to | 09 Oo H b) 0-3-x+ c) O-3+at 2 4 d) O-1 + 3x + 22 4 e) O -3+at 4Let f be a function that has derivatives of all orders on the interval (5, 7). Use the values in the table below and the formula for Taylor polynomials to give the 4th degree Taylor polynomial for f centered at a: : 6: ) f'(5) f\"(5) f\"'(5) WW) 1 7 9 6 4 8,0 1:7[22 6H3\" 6)2 (a: (3)3 its (3)4 b) Ol+7(a:+6)+9(:c+6}26[a:+)34(a:+6)4 c) O1+7{2:+6)+%(2:+6)2(2:+6)3%(a:+6)4 a) O4m46z3+9:r:2+7.7:1 1 9 e)Ox4I3+ 2 6 Ea: +7:r:l 1) O71+7(376)+9{a:76)276(376)?'74(376? Let P\" be the nth Taylor Polynomial of the function at) centered at :r = 0. Assume that f is a function such that l fl\") (x) '5 l for all n and a: (the 1 1 sine and cosine functions have this property.) Estimate the error if P5 (1) is used to approximate f (a ).