Question

Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 7x cos(2x2) (c) Use part (b) to find a power series for AUX) - 1621) 1x) - -1) ( 2.6 +1 +3 What is the radius of convergence, R? R-6 Find the Maclourin series for FUX) using the definition of a Maclaurin series. Assume that f has a power series expansion. Do not show that Ra(x) +0.1 Rox) = sin( Find the associated radius of convergence R.

Answer 1

Given woven we onicos (4x), ao a= 0 f(x) = 7 using raclausin serier #w): 40) 40 a 44n't found 14! ) tw. 7. Cos (1 f'(x) = 72. (sin(x)) (1 2. 2x) + cos(x). 7 ) t'lon) - – 72. Sin (x) x + 7 Cos (1 – zu sin (2) + 7 cos(x) f(0) = 0 + 7 costo) – 7 ... f(a) – – zu cos (n). (2x) – 7 sin (22). 20 - 7 sin(x). 2. 20 - – 7x3 cos ( 1 ) - 14x. Sin (2) - 72 sin ( x )

– 7x3 cos (ar) – 21 x sin ( x ). &(o) - 0 - 0 - 0 f(x) = - + x (-sin (1x)). 4:21 -7 cos(xv). 3x – 21 (v. cos(x). . m + sin (2x) 7 sie (2 ) – 21. 2 cos(x) - 21 x cos(x) – 21 sie (in). 7 sin (2x) – 42 x cos (2) – 21. Since) f(0) = 0 – 42.(0) – 0 = 0. to - 74. cos(x) x + 7 sin (r) 43 - 42 x (sin(er)). – 42 cos (1x): 24 - 21 cos(x). x. 7x5 cos (2x) + 28 43 sin (r). + 42 x lin (2) - 08:105 x. Los (14)

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