6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)³ + 6(x – 4)+ be the Taylor polynomial of degree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)|< 24 for all x in the interval [4, 4. 3] a) Find the values of f(4) and f''(4). b) Approximate f(4.3) using the 4th degree Taylor polynomial given above. What is the maximum possible error in making this estimate? Give FOUR decimal place accuracy for both the approximate value and the error bound. c) Use your answer to part b) to find an interval [a, b] such that a < f(4.3) < b. Give FOUR decimal place accuracy in all number values.

6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)³ + 6(x – 4)+ be the Taylor polynomial of degree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)|< 24 for all x in the interval [4, 4. 3] a) Find the values of f(4) and f''(4). b) Approximate f(4.3) using the 4th degree Taylor polynomial given above. What is the maximum possible error in making this estimate? Give FOUR decimal place accuracy for both the approximate value and the error bound. c) Use your answer to part b) to find an interval [a, b] such that a < f(4.3) < b. Give FOUR decimal place accuracy in all number values.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 17EQ

See similar textbooks

Similar questions

4. Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine the second order Taylor polynomial for x(1) about / == = 0. 5. Establish the approximation
find the taylor polynomials of order 0 1 2 and 3 generated by f(x) =1/(x+5) at x=0
Find the third degree Taylor Polynomial centered at x = 0 for f(x) = x^2√1 + 4x.
What would be the Taylor polynomials of orders 0,1,2, and 3 generated by f(x) = ln(5+x) when x=6?
1. determine the second-order Taylor approximation of the polynomial p(x) = x^5 + 6x^4 + x^2 − 1 at the points x = 0 and x = 1.
Express the 4th Taylor polynomial of the function f (x) = e3x at the neighborhood a = 1.
Let f(x)=8x+2ln(x). Find a second degree Taylor polynomial about c=1 and use P2(x) to approximate 16+2ln(2) with determining a bound for the error of the approximation.
let f(x) = cos(x) and x0 = 0. Find the Taylor polynomial of degree N = 4.
The Taylor polynomial of order 2 generatedby a twice-differentiable function ƒ(x) at x = a is called thequadratic approximation of ƒ at x = a., find the(a) linearization (Taylor polynomial of order 1) and (b) quadraticapproximation of ƒ at x = 0. ƒ(x) = ln (cos x)
Consider a function f(x)and its second Taylor polynomial P2 (x) centered at a .if p2x is not constant and has a maximum at a then fx is maximum at a
4). Find the Taylor polynomial of degree two approximating the given function centered at the given point. f(x) = 1 x at a = 1 p2(x) = PLEASE SHOW STEP BY STEP CLEARLY