Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)3 + 6(x – 4)+ be the Taylor polynomial ofdegree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)| < 24 for all x inthe 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 themaximum possible error in making this estimate? Give FOUR decimal place accuracy for boththe 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. GiveFOUR decimal place accuracy in all number values. 7) Let f be the function defined by f(x) =1+xa) Write the first four terms and the general term of the Maclaurin series for f(x)centered at x = 0.b) Find the interval of convergence for the Maclaurin series for f(x).c) Use the result from part a) to find the first four terms and the general term of theseries for g(x) = In |1 + x| centered at x = 0.[HINT: How can you get to In |1+x| from ?]1+xd) Find the interval of convergence for the series you created in part c).

Name: Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² –
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)3 + 6(x – 4)+ be the Taylor polynomial ofdegree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)| < 24 for all x inthe interval [4, 4. 3]a) Find t

Note: According to bartleby we have to answer only first question please upload the question…

Math

Advanced Math

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).

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).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 19E

See similar textbooks

Similar questions

find the taylor polynomials of order 0 1 2 and 3 generated by f(x) =1/(x+5) at x=0
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 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