(1 point) Consider the function f(x) = f* cos(t) – 1 dt. t2 Which of the...
(1 point) Consider the function f(x) = Es cos(t) – 1 t2 dt. Which of the following is the Taylor Series for f(x) centred at x = 0? 2n-1 Α.Σ (-1)" (2n – 1)(2n)! X +C. n=0 oo 2n-1 B. (-1)" (2n – 1)(2n)!" X n=1 (-1)" X20-2 (2n + 1)! M n=1 D. iM: (-1)"(2n – 2), 2n–3 (2n)! X n=1
point) Consider a function f(x) that has a Taylor Series centred at x = 5 given by ſan(x – 5)" n=0 he radius of convergence for this Taylor series is R= 4, then what can we say about the radius of convergence of the Power Series an ( 5)"? nons A. R= 20 B.R= 8 C. R=4 D. R= E. R= 2 F. It is impossible to know what R is given this information. point) Consider the function f(x) =...
(1 point) Consider the function cos(t) f(x) = dt. Which of the following is the Taylor Series for f(2) centred at x = 0? O (-1)" A. 2n-1 (2n - 1)(2n)! O B. (-1)" (2n – 1)(2n)! 2n-1 +C n0 O C. (-1)" 220-2 (2n +1)! (-1)"(2n - 2) (2n)! D. n=1 2n 3
f(x) = | (1 point) Consider the function cos(t) - 1 dt. Which of the following is the Taylor Series for f(x) centred at 2-07 A (-1)"(2n - 2). 2-3 (2n) B. (-1)" (2n - 1)(2n)! 2-1 + C. no ho 2n-1 (-1)" (2n - 1)(2n)! (-1)"_222 D. (2n +1)!
Problem 12. (1 point) Consider the function f(0) = %,* cos(t) – 1 dt. +2 Which of the following is the Taylor Series for f(2) centred at x = 0? O (-1)" A. n1 (2n – 1)(2n); 22n-1 (-1)"(2n - 2) B. n1 22n-3 (2n)! (-1) C. n0 -22n-1 +C (2n-1)(2n)! D. (-1) 2n-2 1 (2n +1)!
Problem 11. (1 point) Consider the following series Σ 3n2 + 10n6 876 - 772 ). If we were to calculate the limit L needed to run the Root Test, which of the following values would we get? A. L= // B. L = C. L = 1. D. L = 10 E. It diverges Problem 12. (1 point) Consider the function f(x) = cos(t) - 1 dt. 12 Which of the following is the Taylor Series for f(x) centred...
(1 point) Consider a function f(x) that has a Taylor Series centred at x = -3 given by an(x + 3)" n=0 If the radius of convergence for this Taylor series is R = 4, then what can we say about the radius of convergence of the Power Series Š an -(x + 3)" ? no n=0 A. R= 2 4 OB.R = 6 OC. R = 4 OD. R = 24 O E. R= 8 F. It is impossible...
Problem 9. (1 point) Suppose that the function f(x) is equal to the convergent powers series Σ 3+1 n! -(x – 6) 30+2 Which of the following is equal to the value of f(14) (6)? -14! 4! B.O. 35 c. 4!" 315 D 14! E. 35 Problem 10. (1 point) Determine the Taylor Series of the function f(x) = 9x? (1 − x)2 centred at x = 0. Α. Σ(-9)",ία. 9 Β. x843 Η + c. Σ9" x2η. O D....
Problem 13. (1 point) Consider a function f(x) that has a Taylor Series centred at x = -1 given by 00 3 4. (x + 1)" HO If the radius of convergence for this Taylor series is R = 2, then what can we say about the radius of convergence of the Power Series Σ ax (x + 1)"? ns 2 IOARE B. R = 10 C. R=4 D. R=1 E. R= 2 F. It is impossible to know what...
The sketch of the following periodic function f (t) given in one period f(t) t2 -1, 0s t s 2 is given as follows f(t) 2 -1 We proceed as follows to find the Fourier series representation of f (t) (Note:Jt2 cos at dt = 2t as at + (a--)sina:Jt2 sin at dt = 2t sin at + sin at. Г t2 sin at dt-tsi. )cos at.) Please scroll to the bottom of page for END of question a) The...