Chapter 11.11, Problem 15E
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Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
Solutions
Chapter
Section
BuyFindarrow_forward
Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem
- (a) Approximate f by a Taylor polynomial with degree n at the number a.
- (b) Use Taylor’s Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval.
- (c) Check your result in part (b) by graphing | Rn(x) |.
15. f(x) = x2/3, a = 1, n = 3, 0.8 ≤ x ≤ 1.2
(a)
To determine
To approximate: The function
Explanation
Formula used:
Taylor polynomial:
Let nth degree Taylor polynomial of f at a is denoted by
And f is the sum of its Taylor series,
Calculation:
The given function is
Then,
The first derivative of
The second derivative is
The third derivative is
(b)
To determine
To estimate: The accuracy of the approximation
(c)
To determine
To check: The result in part (b) by graphing
Chapter 11 Solutions
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A researcher plans to select a sample from each of the following populations. Which is likely to be a probabili...
Research Methods for the Behavioral Sciences (MindTap Course List)
Express each of the following pairs of signed numbers as absolute values and subtract the smaller absolute valu...
Mathematics For Machine Technology
Each equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identit...
College Algebra (MindTap Course List)
The Scholastic Aptitude Test (SAT) consists of three parts: critical reading, mathematics, and writing. Each pa...
Statistics for Business & Economics, Revised (MindTap Course List)
Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are sh...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
