Consider the following data set generated by a function, f(x): X 0.0 0.2 0.4 f(x) 1.03...

 

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Consider the following data set generated by a function, f(x): X 0.0 0.2 0.4 f(x) 1.03 1.23 1.53 1. [6 Marks] Find the interpolating polynomial for the above data of appropriate order using Newton's Divided/Difference method. 2. [1 Mark] Use the interpolating polynomial to find the approximate value of f(0.37). 3. [4 Marks] Add a data point f(0.8) = 1.83 to the given data, and find the new interpolating polynomial that includes this new data point. Consider the following data set generated by a function, f(x): X 0.0 0.2 0.4 f(x) 1.03 1.23 1.53 1. [6 Marks] Find the interpolating polynomial for the above data of appropriate order using Newton's Divided/Difference method. 2. [1 Mark] Use the interpolating polynomial to find the approximate value of f(0.37). 3. [4 Marks] Add a data point f(0.8) = 1.83 to the given data, and find the new interpolating polynomial that includes this new data point.