can you please show the answer clearly! (0) - / ν 2 - αι. Which of...
Determine the Taylor Series for the function f(x) = e-3 centered at α = -1. ΑΣ-3)* * (t+ 1): Β. Σ" (a + 1): «Σ " (a + 1)" b. Σ-30" d';" Σε «-): Ε Σ - 1): Using the Maclaurin Series for et, which of the following series sums to the ΑΣ ΣΕ «ΣΗ Σ 8
(1 point) Determine the Taylor Series of the function f(x) = - 8x2 (1 − x)2 centred at x = 0. Α. (-8)" x2η. n=1 ΧΟ 8 Β. r743 η + 1 n=0 0 c. Σ 8" x2η. n=1 ΧΟ 8x2n+2 n=1 Ε. Σ 8nx+1. n=1
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....
3 only Ex. 3.2. Determine the values of x € R for which the following series con- verge pointwise. 2η (1) Σ2nα (ii) 2η 1+ 2η (2+1)2η n=0 n=0. Με Με Με n=0 | 3η (8) Σ" hete") (vi) Σ. (vii) Σ α ” ln(") n=1 (1) Σεπ 1η-2η 1+0202 = 1
can you please do the steps clearly! 9005 f(x) = Q: find the taylor series (17x) at x=0
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) =...
Problem 1: Which of the following represents a power series representation about x = 0 α5 for the function f(x) 3 +02 X 12m+5 α2(n+5) (Α)Σ (Β) Σ (C) Σ (-1)*2m+5 3η 3n+1 3η n=0 n=0 n=0 X (D) Σ(-1)*2-21+5 (E) Σ (-1)*x2(n+5) 3n+1 3n+1 n=0 n=0
Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
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 the function f(x) = f* cos(t) – 1 dt. t2 Which of the following is the Taylor Series for f(x) centred at x = 0? w A. (-1)" (2n – 1)(2n)! -x2n- +C. n=0 (-1)"(2n – 2) 2n–3. B. (2n)! n=1 c. Σ (-1)" (2n + 1)! -x2n-2 n=1 D. Š (-1)" -X2n-1 (2n – 1)(2n)! n=1