- (a) Show that the function defined by
is not equal to its Maclaurin series.
- (b) Graph the function in part (a) and comment on its behavior near the origin.
Trending nowThis is a popular solution!
Chapter 11 Solutions
CALCULUS,MULTIVARIABLE-W/ACCESS>CUSTOM<
- The question is to find a power series for the function centered at c f(x) = 5/(5-x) , c = -3arrow_forwardFIND THE TAYWR SERIES FUR f (x) = 7 ABOUT x=-3 X4arrow_forwardObserve the function X f(x) = (1+2x)² In order to find the power series for this function, complete the following steps: 1 1-x a. Start with the series Σ. Replace x with (−2x) in this series and k=0 write the corresponding power series for = 1 1+2x b. Take derivative of the series from part (a) above and relate it to the power series for the function 1 (1+2x)²· c. Multiply both sides of the resulting series from above with x, and obtain the series for Write the first four non-zero terms of this series. X (1+2x)² d. What is the radius of convergence for this series? What is the interval of convergence?arrow_forward
- 3arrow_forward(1 point) Write the Taylor series for f(æ) = sin(x) at z = as Find the first five coefficients. C2= C3=arrow_forwardQ1. Find (i) the Fourier cosine series and (ii) the Fourier sine series of the function f(x) = x, 0arrow_forwardExpand f(x) = In x in powers of (x-1) using Taylor's Series. Compute In 1.2. Step 1: Write the given function f (x) = Step 2: Get its derivative (at least until fourth derivative) f (x) = f"(x) = f"(x) = fV (x) = Step 3: Let a = 1 (From x-1, where a =1) f (1) = f' (1) = = (1) ייr fV (1) = Step 4: Recall Taylor's Series and substitute values of f(0), f (0), r'(0) .. f'(a)(x=a), f"(a)(x-a)² f"(a)(x=a)³ 1! f"(a)(x-a)" f(x) = f (a) + +...+ 2! 3! n ! f(x) = Step 5: Try to represent it in summation. f(x) = sin (x) = Eo() Step 6: Evaluate In 1.2. Using the series, let x= 1.2. Use your calculator for checking. f(1.2) = In (1.2) =arrow_forwarda) Find the required Fourier series for the given function. (b) Sketch the function graph to which the series converges over three periods. Q34arrow_forwardFind the power series centered at 0 for the function f(x) = ln(x2 + 1) / x2 .arrow_forwardarrow_back_iosarrow_forward_ios
- 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