convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2.5.8 (3n-1) (x 1) Find the radius of convergence of A. B. 4/3 C. 3/4 I),2 D. O E. 3/2 O F. 1/2 О н. 2/3 convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2...
Find the interval of convergence of the series. (x - 2)" 3n+ 3 - O A. K<3 OB. 1<x<3 O C. - 15x<5 OD. 1sx<3
Find the radius of convergence of 2"n!(x - 1)" n=02-6.10...(4n+2)
19. . 20 . 21 Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = e-3x f(x) = Σ n = 0 Find the associated radius of convergence R. R = Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) = 0.] f(x)...
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
(4) Let(an}n=o be a sequence in C. Define R-i-lim suplanlì/n. Recall that R e [0,x] o0 is the radius of convergence of the power series Σ a (z 20)" Assume that R > 0 (a) Prove that if 0 < ρ < R, then the power series converges uniformly on the closed (b) Prove that the power series converges uniformly on any compact subset of the disk Ix - xo< R (4) Let(an}n=o be a sequence in C. Define R-i-lim...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
Find a power series representation for the function. f(x) = فيه (x – 4)2 00 f(x) = Σ no Determine the radius of convergence, R. R = Evaluate the indefinite integral as a power series. Je at c+ Σ ΦΟ η = Ο What is the radius of convergence R? R = Find the radius of convergence, R, of the series. 3n Σ n! n=1 R= Find the interval, 1, of convergence of the series. (Enter your answer using interval...
2x-1= 0 11. Find the radius of convergence of 112. 3(x+1) (x+2 (Intllip Int 3/16 12. Find the Maclaurin series for f(x) = showing how you got it. Plx) = ax flo)=4 u
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the power series is 3. Find the radius of convergence R2 for f"() Also find the appropriate power series for f"(2). (b) (10) Let z 16i. Find a formula for each of the two square roots z0, 31 of z. Graph both square roots in the complex plane, and identify each. 0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the...
Given functions f(1) = I 2-4 Find I+2 a) f(-x) b) f(x – 3) c) f(x +h) +4 d) f(3) e) is -2 excluded from th domain. Why. Explain.