Chapter 10, Problem 71RE

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.

a. 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=

Find the series' interval of convergence and, within its interval, the sum of the series as a function of ?x.

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?

Find the first four terms of the Taylor series for xcos(2x).