Combining power series Use the power series representation
to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.
36. g(x) = x3 ln (1 − x)
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Use the power series = (-1)"x" to determine a power series centered at 0 for the function f(x) = - %3D (8x + 1)2 8r +1 O Eo(-8)"(n– 1)x"-1 O Eo(-8)"zx"-1 O Eo(8)">x" O Eo(8)"zx"-1 O Eo(-8)"x"arrow_forwardSolve for the following (Power Series)arrow_forwardFind a power series for the function, centered at c. 4 f(x) = 3x + 2' f(x) = Determine the interval of convergence. (Enter your answer using interval notation.) (#) 5 13arrow_forward
- Q// Consider the two series such that: f(x) = 1 + 2x + 3x2 +4x3 + ... and g(x) = 1 + 2x + 3x2 +4x3 + a. Find the sum of the two generating functions. Then find the generating function for the result. b. Find the product of the two generating functions. Attach File Browse My Computerarrow_forwardx²- Q6/ Find five terms of Maclaurin series for f(x) = (1 +x)K where (k) is any Real number, then find exact and approximate value of function if x = 1, k= 2 Ans./ f(x) = 1+ kx + k(k-1) k(k-1)(k-2) „3 1 k(k-1)(k-2)(k-3) ,4 2! 3! 4! @ x = 1 & k = 2 - Exact = 4 Аpproximate 3 4 Q7/ a) Find the first four nonzero terms of Maclaurin series for f (x) = e-x² b) Find the approximate value of the function in part (a) at x = and compare it with exact value? 2x2 12x 120x6 Ans./ a) f(x) =1- 2! +... 4! 6! 2 - Exact = 0. 64118 3 b) @ x == Approximate = 0. 6396 Q8) Considered that the function f(x) = x.e* i. Find the first three nonzero terms in Maclaurin series Compute the approximate value of function (Maclaurin series) at x = 1 and compare it with the exact value? Compute the approximate integral value of the function (Maclaurin series), ii. iii. Ans./ i)f(x) = x + x² +;x³ + ... ii) @ x = 1 - Approximate = 1+ 12 +1³ = 2.5 Exact = 1* e' = 2.7 iii) Integral = 0.958 Q9/ Answer the following points i.…arrow_forwardwrite expansion of function as a power seriesarrow_forward
- Use the power series to find a power series for the function, centered at 0. -2 x² 1 h(x) = ∞ 1 ₁ + x = (-1)"x", |×| < 1 1 n = 0 h(x) n = 0 = = 1 1 + x + 1 1 - X Determine the interval of convergence. (Enter your answer using interval notation.) |(−1,1)arrow_forwardhow do i solve the attached calculus question?arrow_forwardQ/ for 8 ER, use the power series for the exponential function e² to show that (-1)" g2n + iΣn=0 eit = En= 2n=1 (2n)! (-1)" (2n + 1)! 82n + 1arrow_forward
- Use the power series 00 1 E(-1)"x". > |x| < 1 1+ x n = 0 to find a power series for the function, centered at 0. -2 1. 1 h(x) = + x? - 1 1 +X 1- x h(x) = E n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)arrow_forwardFind the radius of convergence of the power series. (-1)"x" En=0| SMarrow_forward∞ Σx" for x < 1 to expand the function in a power series with center c = 0. n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Use the equation 1 1- x 6 1x4 =arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning