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Example 1 Complete the divided difference table for the data used in Example 1 of Section 3.2, and reproduced in Table 3.10 and construct the interpolating polynomial that uses all these data. Table 3.10 f(x) Solution The first divided difference involving xo and x is 0.7651977 0.6200860 f\xi]- flxo]0.6200860 – 0.7651977 1.3 – 1.0 1.0 1.3 f[xo, x1] = -0.4837057. XI - Xo 1.6 0.4554022 1.9 0.2818186 The remaining first divided differences are found in a similar manner and are shown in the 2.2 0.1103623 fourth column in Table 3.11.

Example 1 Complete the divided difference table for the data used in Example 1 of Section 3.2, and reproduced in Table 3.10 and construct the interpolating polynomial that uses all these data. Table 3.10 f(x) Solution The first divided difference involving xo and x is 0.7651977 0.6200860 f\xi]- flxo]0.6200860 – 0.7651977 1.3 – 1.0 1.0 1.3 f[xo, x1] = -0.4837057. XI - Xo 1.6 0.4554022 1.9 0.2818186 The remaining first divided differences are found in a similar manner and are shown in the 2.2 0.1103623 fourth column in Table 3.11.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 57E
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Question Example 1 Complete the divided difference table for the data used in Example 1 of Section 3.2, and reproduced in Table 3.10 and construct the interpolating polynomial that uses all these data. Table 3.10 Solution The first divided difference involving xo and x is f(x1]- f[xo]_ 0.6200860 – 0.7651977 1.3 – 1.0 f(x) 1.0 0.7651977 1.3 0.6200860 f[xo, x1] = -0.4837057. XI - Xo 1.6 0.4554022 The remaining first divided differences are found in a similar manner and are shown in the fourth column in Table 3.11. 1.9 0.2818186 2.2 0.1103623
Transcribed Image Text:Question Example 1 Complete the divided difference table for the data used in Example 1 of Section 3.2, and reproduced in Table 3.10 and construct the interpolating polynomial that uses all these data. Table 3.10 Solution The first divided difference involving xo and x is f(x1]- f[xo]_ 0.6200860 – 0.7651977 1.3 – 1.0 f(x) 1.0 0.7651977 1.3 0.6200860 f[xo, x1] = -0.4837057. XI - Xo 1.6 0.4554022 The remaining first divided differences are found in a similar manner and are shown in the fourth column in Table 3.11. 1.9 0.2818186 2.2 0.1103623
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