Question5. Let f(x) = cos x, Xo = 0, x, = 0.6, and x2 = 0.9. (a) Use cardinal/base functions to construct the Lagrange interpolation polynomial of degree at most two to approximate f. Use cos(0.6) = 0.8 and cos(0.9) = 0.6.
Question5. Let f(x) = cos x, Xo = 0, x, = 0.6, and x2 = 0.9. (a) Use cardinal/base functions to construct the Lagrange interpolation polynomial of degree at most two to approximate f. Use cos(0.6) = 0.8 and cos(0.9) = 0.6.
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![Question5. Let f(x) = cos x, Xo = 0, x1 = 0.6, and x2 = 0.9.
(a) Use cardinal/base functions to construct the Lagrange interpolation polynomial of degree at most two to approximate f. Use cos(0.6) =
0.8 and cos(0.9) = 0.6.
(b) Use the theorem expressing Lagrange interpolation to find an error bound for the approximation on [O, 0.9].
(c) Use Neville's method to construct the interpolation polynomial of degree at most two to approximate f. Use cos(0.6) = 0.8 and cos(0.9) =
0.6. (construct Neville's table)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd2a6003-c37e-4f87-a4db-7e4fe43f88ec%2Fd28fb9fa-7475-45da-8ca7-90795c93cd3b%2Faj19305_processed.png&w=3840&q=75)
Transcribed Image Text:Question5. Let f(x) = cos x, Xo = 0, x1 = 0.6, and x2 = 0.9.
(a) Use cardinal/base functions to construct the Lagrange interpolation polynomial of degree at most two to approximate f. Use cos(0.6) =
0.8 and cos(0.9) = 0.6.
(b) Use the theorem expressing Lagrange interpolation to find an error bound for the approximation on [O, 0.9].
(c) Use Neville's method to construct the interpolation polynomial of degree at most two to approximate f. Use cos(0.6) = 0.8 and cos(0.9) =
0.6. (construct Neville's table)
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