Consider the function f(x) = V1+ V and the three data points or nodes x, =...

 

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Consider the function f(x) = V1+ V and the three data points or nodes x, = 1, x, = 1.5 and x, = 2. %3D a. Construct (by hand) the quadratic Lagrange polynomial L(x) that interpolates to f(x) = V1+ Va for the given nodes. (You can write this out without simplifying terms.) b. What is the interpolated value of L(x) for x = 1.75? Compare this with the exact value of f(1.75). What about for x = 3? (You can use a calculator or software to simplify polynomial and function evaluations.) Consider the function f(x) = V1+ V and the three data points or nodes x, = 1, x, = 1.5 and x, = 2. %3D a. Construct (by hand) the quadratic Lagrange polynomial L(x) that interpolates to f(x) = V1+ Va for the given nodes. (You can write this out without simplifying terms.) b. What is the interpolated value of L(x) for x = 1.75? Compare this with the exact value of f(1.75). What about for x = 3? (You can use a calculator or software to simplify polynomial and function evaluations.)