Question

determine which answer to put by saying the answer is A,b,c or d

and what to write in the two boxes below

This Question: 1 pt Consider the function f(x)=5 tan -(x). a. Differentiate the Taylor series about for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer below. O A. 25** - 25x^4 + 25x24 - 25x34 + O B. 6x?+ 5x98 x25, 5x05 OC. – 25x* + 25x?4 – 25x24 + 25 OD. 573_ 5XLSx25 _ 5x98 .. b.f'(x)= C. The interval of convergence of the power series of f'(x) is (Simplify your answer. Type an inequality or a compound inequality. Type an expression using x as the variable.)

Answer 1

# We know that I = -x + x²x3 + xt.... H2 = 1- x2 + (62) ² (²) 3+ (2)4 - ... - 1x² + x4 a6+28 _ x0+.. mtegrating a both sides wegel da Ist da sci-x² + x4 – x64 x 8 x 10 ... – loa 4 = 7- #18 tant x = - Substituting as implace of a we get tam (25) = -5 -65)+(2S) - S 03_.... multiplying with 3 we get 5 tremi (25) = 548-5294 sets - 5+ sense.... 7 Differentiating (1) with respect to x we get- d (stan (x)) = (5x8-sals at 52 - 53...] = 5.65**)- Ş (05-24) +5 (25:24-(35.7%+- dx a b) =9564 -95244 95227952346-.. f'() = 9524-25x+4 +95 +24_25234+.. f(x) = 9524(1-4104220_7207...)=2594 1+ to

.... LE +*2173+... 14X I 1- x10 + 2 x 30 x 40 1210 1-20 +220 +240 - f'(x)= 25x4 1+ g. 10 On-E 255 0 95 x 425 x 14 4 250 24 – 25 234 + ... = 25 Elon = 25 c m,100-6 430- Let laston von +41 lank 125 (nt non-sl l antil = 1254 +1)-61- 25 (8) 100+49 Man) = lim 1 anti a lim (xol ma anlm- a 8x101 By Rateo test the series converges of 1101 <1 | 1x10 <1 = $1 <1. : The series f'(x) converges if lal <1.