Given the partition To 0, 0.05. 0.1. of the interval [0.0.1] and f(x)= (a) Find an...

 

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Given the partition To 0, 0.05. 0.1. of the interval [0.0.1] and f(x)=² (a) Find an approximation to f(0.07) using Newton's difference polynomial. P(x) that interpolates all the (7) points. Use functional and computed values that are correct to four decimal places. (b) Find an approximation for 1.1 (2) dr by evaluating P(x) dr. (c) Compute o f(x) dr analytically and find the actual error in the approximation in (b) above. (10) [25] Given the partition To 0, 0.05. 0.1. of the interval [0.0.1] and f(x)=² (a) Find an approximation to f(0.07) using Newton's difference polynomial. P(x) that interpolates all the (7) points. Use functional and computed values that are correct to four decimal places. (b) Find an approximation for 1.1 (2) dr by evaluating P(x) dr. (c) Compute o f(x) dr analytically and find the actual error in the approximation in (b) above. (10) [25]