Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR(X)I. y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 X X y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.9 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 1.0 1.1 0.9 M 1.1 1.2 1.2 X X
Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)= T(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing IR(X)I. y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 y -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 X X y 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.9 -0.00002 -0.00004 -0.00006 -0.00008 -0.00010 -0.00012 1.0 1.1 0.9 M 1.1 1.2 1.2 X X
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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