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Construct the natural cubic spline interpolant s(x) to the function ƒ(x) = x² cos(x) — 3x = 0.2 and 2 = at the points xo = 0.1, x₁ (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x2) = 0. : 0.3. Recall that we need: =

Construct the natural cubic spline interpolant s(x) to the function ƒ(x) = x² cos(x) — 3x = 0.2 and 2 = at the points xo = 0.1, x₁ (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x2) = 0. : 0.3. Recall that we need: =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 19E
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Cubic spline

[2] Construct the natural cubic spline interpolant s(x) to the function f(x) = x² cos(x) - 3x at the points xo = 0.1, x₁ = (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x₂) = 0. 0.2 and ₂ = = 0.3. Recall that we need:
Transcribed Image Text:[2] Construct the natural cubic spline interpolant s(x) to the function f(x) = x² cos(x) - 3x at the points xo = 0.1, x₁ = (i) s(x) to interpolate f(x) (ii) s(x), s'(x) s"(x) to be continuous (iii) s"(x) = s"(x₂) = 0. 0.2 and ₂ = = 0.3. Recall that we need:
(a) Approximate f(0.18) and f'(0.18) using s(x) and s'(x), respectively, and list the relative errors. (b) Approximate ƒ'(0.2) using s'(x). Do the values ƒ'(0.2) and s'(0.2) agree? Based on the definition of a cubic spline, should they agree?
Transcribed Image Text:(a) Approximate f(0.18) and f'(0.18) using s(x) and s'(x), respectively, and list the relative errors. (b) Approximate ƒ'(0.2) using s'(x). Do the values ƒ'(0.2) and s'(0.2) agree? Based on the definition of a cubic spline, should they agree?
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