Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition
5th Edition
ISBN: 9780133311617
Author: Prentice Hall
Publisher: Prentice Hall
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Explain how to determine whether a Taylor series for a function f converges to f.
Find the first four non-zero terms of the Taylor series for the function f(x)= cos(-2x)
For x near a = t. Build your terms "from scratch", do not use a series that you already know.
3.
Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1
a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1
b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1
c. Determine the interval of convergence for the series given in (b).
d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.
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- I send the question a second time and pay for each question. Can I explain to you how to write the answer correctly? How can I explain that you write by hand, it is very bad and unreadable? Please give the final answer and you already answered it wrong.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_forwardFind the series' interval of convergence and, within its interval, the sum of the series as a function of ?x.arrow_forward
- Observe 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_forwardFind the first four terms of the Taylor series for xcos(2x).arrow_forward
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