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Consider the differentiation formula S'(X) = (₁/(² + 4) + ₁/(x − 2)). If the formula is derived as in Remark 6.1 using Lagrange interpolation, then the coefficients have the form P₁ = 1/33 with certain numbers s,ter. What is s+t? (Please double-check that you don't get any signs wrong.) O a. -2 O b. -1 О с. 0 O d. 2 O e. 4 O f. -2h Og. h Oh. 2h P₁ = Po - S

Consider the differentiation formula S'(X) = (₁/(² + 4) + ₁/(x − 2)). If the formula is derived as in Remark 6.1 using Lagrange interpolation, then the coefficients have the form P₁ = 1/33 with certain numbers s,ter. What is s+t? (Please double-check that you don't get any signs wrong.) O a. -2 O b. -1 О с. 0 O d. 2 O e. 4 O f. -2h Og. h Oh. 2h P₁ = Po - S

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the differentiation formula with certain numbers s,ter. What is s+t? (Please double-check that you don't get any signs wrong.) If the formula is derived as in Remark 6.1 using Lagrange interpolation, then the coefficients have the form S t = 15 3 3 O a. -2 O b. -1 O c. 0 O d. 2 O e. 4 O f. -2h ƒ'(ñ) ≈ ~ 1/1 (₁₁ƒ(x + + h) + Bof(x O g. h Oh. 2h Bo h ==
Transcribed Image Text:Consider the differentiation formula with certain numbers s,ter. What is s+t? (Please double-check that you don't get any signs wrong.) If the formula is derived as in Remark 6.1 using Lagrange interpolation, then the coefficients have the form S t = 15 3 3 O a. -2 O b. -1 O c. 0 O d. 2 O e. 4 O f. -2h ƒ'(ñ) ≈ ~ 1/1 (₁₁ƒ(x + + h) + Bof(x O g. h Oh. 2h Bo h ==
Remark 6.1: the general idea Let [a, b] CR be an interval with a < b, let ī € (a, b), and let ƒ € C¹¹ ([a, b]). To approximate f'(ī), fix pairwise distinct nodes To,..., In € [a, b] and use the interpolation polynomial for the data (Tk, f(Tk))-0 in Lagrange form n p(x) = Σ f(xk)Lk(x), Lk(x) = k=0 to compute the approximation n j=0 j‡k I- - Ij Ik - Ij n f'(ī) ≈ p'(ī) = Σ ƒ (Tk)L'k(ñ). k=0 (6.1)
Transcribed Image Text:Remark 6.1: the general idea Let [a, b] CR be an interval with a < b, let ī € (a, b), and let ƒ € C¹¹ ([a, b]). To approximate f'(ī), fix pairwise distinct nodes To,..., In € [a, b] and use the interpolation polynomial for the data (Tk, f(Tk))-0 in Lagrange form n p(x) = Σ f(xk)Lk(x), Lk(x) = k=0 to compute the approximation n j=0 j‡k I- - Ij Ik - Ij n f'(ī) ≈ p'(ī) = Σ ƒ (Tk)L'k(ñ). k=0 (6.1)
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