Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 11.11, Problem 1PT
To determine

The quadratic approximation for f(x)=x6 at a = 1.

Expert Solution & Answer
Check Mark

Answer to Problem 1PT

Quadratic approximation for f(x)=x6 at a = 1 is d) T2(x)=1+6(x1)+15(x1)2_.

Explanation of Solution

Result used:

The Taylor polynomial of degree n for f about a is, Tn(x)=f(a)+f(a)1!(xa)+f(a)2!(xa)2++fn(a)n!(xa)n. Tn(x) may be used to approximate f(x) for any given x in the interval of convergence for the Taylor series for f about a.

Calculation:

The given function is f(x)=x6.

To find the quadratic approximation, find T2(x) where a = 1.

The Taylor polynomial of degree 2 for f(x)=x6 about a = 1 is,

T2(x)=f(1)+f(1)1!(x1)+f(1)2!(x1)2

Obtain the values of f(1),f(1)and f(1) as follows.

f(x)=x6;f(1)=1f(x)=6x5;f(1)=6f(x)=30x4;f(1)=30

Substitute these values in T2(x)=f(1)+f(1)1!(x1)+f(1)2!(x1)2. Then,

T2(x)=1+61(x1)+302(x1)2=1+6(x1)+15(x1)2

Therefore, the quadratic approximation is, d) T2(x)=1+6(x1)+15(x1)2_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch It
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…
4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of about

Chapter 11 Solutions

Study Guide for Stewart's Multivariable Calculus, 8th

Ch. 11.2 - Prob. 3PTCh. 11.2 - Prob. 4PTCh. 11.2 - Prob. 5PTCh. 11.2 - Prob. 6PTCh. 11.2 - Prob. 7PTCh. 11.2 - Prob. 8PTCh. 11.3 - For what values of p does the series n=11(n2)p...Ch. 11.3 - True or False: If f(x) is continuous and...Ch. 11.3 - Prob. 3PTCh. 11.3 - Prob. 4PTCh. 11.3 - Prob. 5PTCh. 11.3 - Prob. 6PTCh. 11.4 - Prob. 1PTCh. 11.4 - Prob. 2PTCh. 11.4 - True or False: n=1n+n3n2/3+n3/2+1 is a convergent...Ch. 11.4 - Prob. 4PTCh. 11.4 - Prob. 5PTCh. 11.5 - Prob. 1PTCh. 11.5 - Prob. 2PTCh. 11.5 - Prob. 3PTCh. 11.5 - Prob. 4PTCh. 11.6 - Prob. 1PTCh. 11.6 - Prob. 2PTCh. 11.6 - Prob. 3PTCh. 11.6 - Prob. 4PTCh. 11.6 - Prob. 5PTCh. 11.6 - Prob. 6PTCh. 11.7 - Prob. 1PTCh. 11.7 - Prob. 2PTCh. 11.7 - Prob. 3PTCh. 11.7 - Prob. 4PTCh. 11.7 - Prob. 5PTCh. 11.7 - Prob. 6PTCh. 11.8 - Sometimes, Always, or Never: The interval of...Ch. 11.8 - Prob. 2PTCh. 11.8 - Prob. 3PTCh. 11.8 - Prob. 4PTCh. 11.8 - Prob. 5PTCh. 11.9 - Prob. 1PTCh. 11.9 - For f(x)=n=0x2nn!, f(x) = a) n=1x2n1n! b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1, x1x2dx= a) n=0x2n2n b)...Ch. 11.9 - Using 11x=n=0xn for |x| 1 and differentiation,...Ch. 11.9 - From 11x=n=0xn for |x| 1 and substituting 4x2 for...Ch. 11.10 - Given the Taylor Series ex=n=0xnn!, a Taylor...Ch. 11.10 - Prob. 2PTCh. 11.10 - Prob. 3PTCh. 11.10 - Prob. 4PTCh. 11.10 - Prob. 5PTCh. 11.10 - Prob. 6PTCh. 11.10 - Prob. 7PTCh. 11.10 - Prob. 8PTCh. 11.10 - Prob. 9PTCh. 11.10 - Prob. 10PTCh. 11.10 - Using a binomial series, the Maclaurin series for...Ch. 11.10 - Prob. 12PTCh. 11.11 - Prob. 1PTCh. 11.11 - Prob. 2PTCh. 11.11 - Prob. 3PT
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY