Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400126
Author: Raymond Barnett, Michael Ziegler
Publisher: PEARSON+
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Chapter 10.4, Problem 5E
To determine
To find: The error in the approximation of
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8. Find the (only) equation of a polynomial p(x) th
• Root at 0 of degree 1
• Root at 1 of degree 1
• Root at -3 of degree 2
• p(2) = 5
Problem 4. The graph of the function f(x) is shown below:
f
(a) Explain why T3(x) = 1.6 – 0.8(x – 1) +0.4(x – 1)² – 0.1(x – 1)³ cannot be the third Taylor polynomial of f(x)
centered at x = 1.
(b) Explain why T3(x) = 2.8+0.5(x – 2) +1.5(x – 2)2 – 0.1(x – 2)³ cannot be the third Taylor polynomial of f(x)
centered at x =
= 2.
15. Suppose a function f is approximated with a fourth-degree Taylor polynomial about x =1. If the
maximum value of the fifth derivative between x = 1 and x = 3 is 0.01, that is, (5) (x) <0.01, then
the maximum error incurred using this approximation to compute (3) is
(A) 0.054
(B) 0.0054
(C) 0.26667
(D) 0.02667
(E) 0.00267
Chapter 10 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
Ch. 10.1 - Find the nth derivative of f(x)=lnx.Ch. 10.1 - Prob. 2MPCh. 10.1 - Prob. 3MPCh. 10.1 - Find the second-degree Taylor polynomial at a = 8...Ch. 10.1 - Prob. 5MPCh. 10.1 - Prob. 1EDCh. 10.1 - (A)Let p(x) be a polynomial of degree n 1....Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3E
Ch. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - In Problems 1316, find f(3)(x). 15.f(x)=exCh. 10.1 - In Problems 1316, find f(3)(x). 16.f(x)=xCh. 10.1 - Prob. 17ECh. 10.1 - In Problems 1720, find f4(x). 18.f(x)=e5xCh. 10.1 - Prob. 19ECh. 10.1 - In Problems 1720, find f4(x). 20.f(x)=12+xCh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - In Problems 2128, find the indicated Taylor...Ch. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Use the third-degree Taylor polynomial at 0 for...Ch. 10.1 - Prob. 41ECh. 10.1 - Use the third-degree Taylor polynomial at 4 for...Ch. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Prob. 60ECh. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Prob. 64ECh. 10.1 - Prob. 65ECh. 10.1 - Prob. 66ECh. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Consider f(x) = ln (1 + x) and its third-degree...Ch. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Prob. 77ECh. 10.1 - Prob. 78ECh. 10.1 - Prob. 79ECh. 10.1 - Prob. 80ECh. 10.1 - Prob. 81ECh. 10.1 - Average price. Given the demand equation...Ch. 10.1 - Prob. 83ECh. 10.1 - Prob. 84ECh. 10.1 - Prob. 85ECh. 10.1 - Prob. 86ECh. 10.1 - Prob. 87ECh. 10.1 - Prob. 88ECh. 10.1 - Prob. 89ECh. 10.1 - Prob. 90ECh. 10.1 - Prob. 91ECh. 10.1 - Prob. 92ECh. 10.1 - Prob. 93ECh. 10.1 - Prob. 94ECh. 10.1 - Prob. 95ECh. 10.1 - Prob. 96ECh. 10.1 - Prob. 97ECh. 10.1 - Prob. 98ECh. 10.2 - Prob. 1MPCh. 10.2 - Prob. 2MPCh. 10.2 - Prob. 3MPCh. 10.2 - Prob. 1EDCh. 10.2 - (A)The six functions pn(x)=1+x++xn, n = 1, 2, , 6,...Ch. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - (A) Graph the nth-degree Taylor polynomials at 0...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - In Problems 3338, find the nth-degree Taylor...Ch. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - (A) Find the interval of convergence of the Taylor...Ch. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Problems 4750 require a basic knowledge of the...Ch. 10.3 - Prob. 1MPCh. 10.3 - Find the Taylor series at 0 for f(x) = 3x3 ln(1 ...Ch. 10.3 - Prob. 3MPCh. 10.3 - Prob. 4MPCh. 10.3 - Prob. 5MPCh. 10.3 - Prob. 6MPCh. 10.3 - Prob. 7MPCh. 10.3 - Prob. 8MPCh. 10.3 - Prob. 1EDCh. 10.3 - Prob. 2EDCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Solve the problems by performing operations on the...Ch. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Find the Taylor series at 0 for (A) f(x)=x1x2 (B)...Ch. 10.3 - Prob. 35ECh. 10.3 - If f(x) satisfies f(x) = ln (1 + x2) and f(0) = 1,...Ch. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.4 - Prob. 1MPCh. 10.4 - Prob. 2MPCh. 10.4 - Prob. 3MPCh. 10.4 - Prob. 4MPCh. 10.4 - Prob. 1EDCh. 10.4 - Suppose you wish to use a Taylor series for...Ch. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - In Problems 938, use Theorem 1 to perform the...Ch. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - In Problems 4548, use the second-degree Taylor...Ch. 10.4 - Prob. 46ECh. 10.4 - In Problems 4548, use the second-degree Taylor...Ch. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - To estimate 01.511+x2dx a student takes the first...Ch. 10.4 - There are different ways to approximate a function...Ch. 10.4 - There are different ways to approximate a function...Ch. 10.4 - In Problems 5566, use Theorem 1 to perform the...Ch. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Useful life. A computer store rents time on...Ch. 10.4 - Average price. Given the demand equation...Ch. 10.4 - Temperature. The temperature (in degrees Celsius)...Ch. 10.4 - Temperature. Repeat Problem 61 for...Ch. 10.4 - Prob. 63ECh. 10.4 - Prob. 64ECh. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Use Theorem 1 of Section 10.2 to find the interval...Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - In Problems 10 and 11, use the formula an =...Ch. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - In Problems 25 and 26, use the second-degree...Ch. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - In Problems 27 and 28, use a Taylor polynomial at...Ch. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Medicine. The rate of healing for a skin wound (in...Ch. 10 - Prob. 42RECh. 10 - Prob. 43RE
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