(3 marks) In the 17th century, Machin obtained the formula π-arctan (1)-aret an (2,9) - arctain 239 Use the Taylor polynomial of degree 5 to approximate 4 arctan () - arcta235) (3 marks) Explain why...
5. Let f(x)- arctan(x) (a) (3 marks) Find the Taylor series about a 0 for f(x). Hint: - arctan(x) - dx You may assume that the Taylor series for f(x) converges to f (x) for values of x in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(x)? Show that the Taylor series converges at x-1. (c) (3 marks) Hence, write T as a series (d) (3 marks) Go to...
5. Let f(z) = arctan(z) (a) (3 marks) Find the Taylor series about r)Hint: darctan( You may assume that the Taylor series for f(x) converges to f(x) for values of r in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(z)? Show that the Taylor series converges at z = 1 (c) (3 marks) Hence, write as a series. (d) (3 marks) Go to https://teaching.smp.uq.edu.au/scims Calculus/Series.html. Use the interactive animation...
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred at x = 1. Do this in two ways: (a) Use the general formula at the top of page 60--calculating successive derivatives of vx. (b) Change variable so you can directly use the formula of Ex 4.6: 1 17 1/ 11315 (1 + y)1/2 = 1+3y + 2 + - 41 2 y4 + ... ull- 2 2 2 Now we ask how accurate...
13 points SCalcET8 11 11,015 Consider the following function. f(x)-x57, a 1, n-3, 0.7Sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a. T3(x) (b) Use Taylo's Inequality to estimate the accuracy of the a pproximation Rx)· (x) when x lies in the given interval. (Round your answer to eight de IR2(x)I s (c) Check your result in part (b) by graphing IR,(). 0.00015 1.3 0 0.9 1.0 1.1 -0.0000S 0.00010 -0.0001o 0.00005 -0,00015 8...
only parb b. thanks Consider the following function Kx)=x4/5, a = 1, n= 3, 0.9 sxs 1.1 (a) Approximate fby a Taylor polynomial with degree n at the number a. 125 (b) Use Taylor's Inequality to estimate the accuracy of the approximation fx) Tn(x) when x lies in the given interval (Round your answer to eight decimal places.) R3(x)1 s 0.000133X (c) Check your result in part (b) by graphing IRn(x). 2.5 x10-6 2. x 10-6 1.5 x 10-6 1....
question b please Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
all but dont work on the julia box one which is 2 i think so 1-3-4 Fitchburg State University Department of Mathematics Project #3 Math 2400: Calculus II April 11, 2019 project for Calculus II. You may work on this with up to one other fellow student. Answer all questions completely and type or neatly write out. The final project should be turned in by Tueeday, April 23. How is it that we generate For this project it helps to...