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5. Let f(x) = and consider f(x) dx. 1+x² e [ ²₁ ƒ(² (b) Find the Taylor series of f(r). Replace f(x) by its 4th order Taylor polynomial to approximate f(x) dr. Compute error by comparing with the correct value. (c) Interpolate f(x) at n = 7 evenly-spaced points in [-1,1]. Replace f(x) by the interpolating polynomial to approximate ef f(x) dr. Compute error by comparing with the correct value. (a) Evaluate f(x) dx.

5. Let f(x) = and consider f(x) dx. 1+x² e [ ²₁ ƒ(² (b) Find the Taylor series of f(r). Replace f(x) by its 4th order Taylor polynomial to approximate f(x) dr. Compute error by comparing with the correct value. (c) Interpolate f(x) at n = 7 evenly-spaced points in [-1,1]. Replace f(x) by the interpolating polynomial to approximate ef f(x) dr. Compute error by comparing with the correct value. (a) Evaluate f(x) dx.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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5. Let f(x)= 1 1+x² and consider [₁ f(x) dx. (a) Evaluate [ f(x) da. (b) Find the Taylor series of f(r). Replace f(x) by its 4th order Taylor polynomial to approximate f(x) da. Compute error by comparing with the correct value. (c) Interpolate f(x) at n = 7 evenly-spaced points in [-1,1]. Replace f(x) by the interpolating polynomial to approximate eff(r) dr. Compute error by comparing with the correct value.
Transcribed Image Text:5. Let f(x)= 1 1+x² and consider [₁ f(x) dx. (a) Evaluate [ f(x) da. (b) Find the Taylor series of f(r). Replace f(x) by its 4th order Taylor polynomial to approximate f(x) da. Compute error by comparing with the correct value. (c) Interpolate f(x) at n = 7 evenly-spaced points in [-1,1]. Replace f(x) by the interpolating polynomial to approximate eff(r) dr. Compute error by comparing with the correct value.
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