For the function cos(x) f(x) = 0 x 2 1 + sin (x) a) Using...

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For the function cos(x) f(x) = 0 x 2 " 1 + sin (x) a) Using an equispaced set of 10 nodes, generate the Lagrange interpolating polynomial to f(x). Generate a plot which shows how the error in your approximation varies over the interval. b) Using an equispaced set of 20 nodes, generate the Lagrange interpolating polynomial to f(x). Generate a plot which shows how the error in your approximation varies over the interval. c) At what number of equispaced nodes does your Lagrange interpolation approximation break down? d) Does using Chebyshev points help resolve the issues you saw in c) ? Provide examples to verify your claim. For the function cos(x) f(x) = 0 x 2 " 1 + sin (x) a) Using an equispaced set of 10 nodes, generate the Lagrange interpolating polynomial to f(x). Generate a plot which shows how the error in your approximation varies over the interval. b) Using an equispaced set of 20 nodes, generate the Lagrange interpolating polynomial to f(x). Generate a plot which shows how the error in your approximation varies over the interval. c) At what number of equispaced nodes does your Lagrange interpolation approximation break down? d) Does using Chebyshev points help resolve the issues you saw in c) ? Provide examples to verify your claim.

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To prove the equivalence of the statements a and b we will first show that a implies b and then that ... View the full answer