Consider the following data set and the piecewise cubic function {(0,0), (1, 1), (2,5)}, - C(x):...

  

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Consider the following data set and the piecewise cubic function {(0,0), (1, 1), (2,5)}, - C(x): = { x+(181)x(x-1) + (81 +82 2)x2(x 1) - if x [0,1] 1+4(x-1)+(482) (x-1)(x-2)+ (82 + 83 - 8)(x-1)2(x-2) if x = [1,2]. Write down the system of equations defining a clamped spline for the data with endpoint conditions C'(0) = a and C'(2) = B. Consider the following data set and the piecewise cubic function {(0,0), (1, 1), (2,5)}, - C(x): = { x+(181)x(x-1) + (81 +82 2)x2(x 1) - if x [0,1] 1+4(x-1)+(482) (x-1)(x-2)+ (82 + 83 - 8)(x-1)2(x-2) if x = [1,2]. Write down the system of equations defining a clamped spline for the data with endpoint conditions C'(0) = a and C'(2) = B.