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Suppose you know that
and the Taylor series of f centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates f(5) with error less than 0.0002.
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Chapter 11 Solutions
Multivariable Calculus
- CAOUST 9 Write the Taylor Series for f(x) = sin(x) at x = 1/2/2 as p n não Cn (x-7) Find the first 5 coeffecients. 2arrow_forwardThe Taylor series at x = 0 for f(x) = sec x is 1 + £r² + ☆x* + 6+ · … . Find f((0).arrow_forwarda. Find the Taylor series at 0 by performing operations on the basic Taylor series. State the interval of convergence. f(x)=ln(1+16x^2) Type the first four terms and the nth-term of the Taylor series. f(x)= b.Find the Taylor series at 0 by performing operations on the basic Taylor series. State the interval of convergence. f(x)=4/5+x^2 Type the first four terms and the nth-term of the Taylor series. f(x)= c. Evaluating the Taylor series at 0 for f(x)=e^−x at x=0.8 produces the following series. e^−0.8=1−0.8+0.32−0.085333+0.017067−0.002731+⋯ Use two terms in this series to approximate e^−0.8, and then estimate the error in this approximation. e^−0.8=arrow_forward
- What is the limit as x->0 of (sin(2x))/x using the Taylor series?arrow_forwardpart b and c pleasearrow_forward1 (2 + x)(10 − x) - a. Find the Taylor series for f(x) centered at c = 14. Consider the function f(x) = = f(x) = Σ n=0 F b. Find the interval of convergence for the series found in Part a. Interval of convergence: ->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
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