5. Piece-wise cubic polynomial interpolation Using the same setup as problem 4 and 5, if one wishes to estimate f(2) by f(x) where xi xN-2, use the same f would for N-SN-2 as we (a) (13 points) Let [a'-[0.3 and f(z) sin(z). You know the true value of f at the points 0 hi including roN 3. Let Using piece-wise cubic interpolation estimate the value of f at 3. What is the error from the true value? Repeat this exercise with h- . Report the values of all your , , and coefficients in both cases. How do the errors compare? Note, to solve the 4x4 systems, you may write code in any language (for example: existing functions in Matlab or Python with Numpy, C, C++, Java, etc...). You are expected to turn that code in To interpolate onto an entirely new grid, you would need to have a for-loop, with a 4x4 system solve inside each loop 5. Piece-wise cubic polynomial interpolation Using the same setup as problem 4 and 5, if one wishes to estimate f(2) by f(x) where xi xN-2, use the same f would for N-SN-2 as we (a) (13 points) Let [a'-[0.3 and f(z) sin(z). You know the true value of f at the points 0 hi including roN 3. Let Using piece-wise cubic interpolation estimate the value of f at 3. What is the error from the true value? Repeat this exercise with h- . Report the values of all your , , and coefficients in both cases. How do the errors compare? Note, to solve the 4x4 systems, you may write code in any language (for example: existing functions in Matlab or Python with Numpy, C, C++, Java, etc...). You are expected to turn that code in To interpolate onto an entirely new grid, you would need to have a for-loop, with a 4x4 system solve inside each loop