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8. (10 pts) Power Series The term in the power series (-1) (3x - 4) is,...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
1 (10 pts) Use our “brute force technique' for generating a power series representation for f centered about x = 4 if f(x) Write your answer in 3x-3 summation notation. =
1 (10 pts) Use our 'brute force technique' for generating a power series representation for f centered about x = 4 if if f(x)= Write your answer in 3x-3 summation notation.
- 8) Find the interval of convergence for the following power series: no (n+1)(n+a) no (2n)!" 9) Using f(x) = 8 X = 1 hod a power senes representation for the no 1-X given Anchons (a) f(x) = 2 b) 60) = 1 C) KW) = Orctan (x). I 4- 3x3 +3x² 10) Find the taylor polynomial of degree for the fonction f(x) = V15+x. LÔ 0 - 1 = | b) If n o ano then Ean converges True...
Find the interval of convergence of the power series: 5) 00 2n -(4x – 8)" n n=1 E (n + 1)(x - 2)" (2n + 1)! n=0 7) 00 w n(x + 10)" (2n)! n=0
1 and determine the 8. [10 pts Find a power series representation for the function f(:1) = interval of convergence,
Find the radius of convergence of the following power series. IM8 (3x - 10) n 15
Question 25 For which values of a does the following power series converge? 8 (-1) + (x - 1) N N=1 Only for a € (0,2). Only for 3 € (0,2) Only for 3 € (0,2) For all real numbers 2. Only for x = [0,2) Only at 2 = 1 Question 26 Which of the following is the power series representation of the function f(x) = ln(2 + x)? 2N (-1)^-1 2.N N=1 [(-1) vxN 2N N1 2N In(2)...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...