Use the third order Taylor polynomial at 9 to approximate v10 as follows:(a) Explain why 9 is a good tabular point;(b) Give the third order Taylor polynomial about the tabular point and the valueof the approximation;15(c) Show that the error E3(10) is at most4!16 · 37

Third-order Taylor polynomial a) 25 is a good tabular point as the terms in the Taylor series are…

Answered: Jse the third order Taylor polynomial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use a Taylor polynomial of degree 4 to approximate the number √(1.1).
In a hospital, a drug is given to a patient. Let f(t) be the amount of drug (in mg) in the patient's body t minutes after it is administered. The nurses want to predict how the body will absorb the drug (the shape of the graph y = f(t)) to be able to prepare the next course of action. One of them remembers about Taylor polynomials from their Calculus course and explains that they allow to predict the shape of a function by making very accurate measurements of the function at one point. They decide to do this and they find the following details about the patient's absorption of the drug: • f(15) = 140 • f'(15) = -10 • f" (15) = 12 1 000 Use these details to approximate the average amount of drug in the patient's body over the first 2 hours: 120 1 f(e) dt 120 Important: Remember that the measurements were made at t = 15 minutes.
A function ? = ?(?) is given by the following table.X 0 4 7 12 21Y 3 30 61 84 343a) Explain and Construct the divided difference table for the above data and find ?(19.75).b) Find a Lagrange interpolating polynomial which passes through the above points.c) Compute ?(19.75) by Lagrange interpolating polynomial and compare your result with thevalue obtained in (a).
Find the Taylor polynomial T2(x) and compute the error |f(x) – T2(x)| for the given values of a and æ. f(x) = esin(z), a = x = 1.5 (Round your answer to six decimal places.) T2(1.5) = (Round your answer to two decimal places.) |f(1.5) – T2(1.5)| = X10 4
Find the second Taylor polynomial P2(x) for the function f(x) = √4 + xabout x0 = 0. Approximate √3.9 using P2(x). Find the absolute error and the relative error for the approximation (you can use your calculator to find the “exact” value for √3.9).
K a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. X Approximate √1.02 using f(x)=√1+x and p₂(x) = 1 + 2 x² 8 a. Using the Taylor polynomial p₂, √1.02~ (Do not round until the final answer. Then round to four decimal places as needed.)
Use the remainder term to estimate the absolute error in approximating the following quantity with the nth-order Taylor polynomial centered at 0. tan 0.31, n = 2 Select the correct choice below and fill in the answer box to complete your choice. (Use scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to two decimal places as needed.) O A. Error OB. Error OC. Error O D. Error O E. Error 16 3 for M = 0.31 for M = for M = 0 for M = 2 1 π for M:
Basic Calculus will give thumbs up for the help! Pls help answer:
Suppose you use a second-order Taylor polynomial centered at 0 to approximate a function ƒ. What matching conditions are satisfiedby the polynomial?
Given the function f(x) = 1/√(x): (a) Find a third-degree Taylor polynomial for f centered at x= 1. Show your work for any credit. (b) Use your Taylor polynomial to estimate1/√(0.15625). Report your answer with at least 5 digits after the decimal place. (c) Estimate the error using the remainder theorem. Show your work for any credit. Justify your choice of M in your computation. Report your answer with at least 5 digits after the decimal place.
a) Use the Taylor polynomial for f(x) = sqrt(x) of degree 2 at point 100 to find an approximate value for sqrt(101). And then give an estimate of the inaccuracy of the value found. b) Justify whether the approximate value found in (a) is too large or too small compared to the real value of sqrt(101)
a. Approximate the given quantity using Taylor polynomials with n = 3. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. 0.11 a. P3 (0.11) ~ (Do not round until the final answer. Then round to seven decimal places as needed.) b. absolute error (Use scientific notation. Use the answer from part a to find this answer. Round to two decimal places as needed.)

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Jse the third order Taylor polynomial at 9 to approximate v10 as follows: (a) Explain why 9 is a good tabular point; (b) Give the third order Taylor polynomial about the tabular point and the value of the approximation; 15 (c) Show that the error E3(10) is at most 4!16 · 37*