The data for Exercise 6 were generated using the following functions. Use the error formula to find a bound for the error, and compare the bound to the actual error for the cases n = 1 and n = 2.
Reference: exercise 6
Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following:
a. f (0.43) if f (0) = 1, f (0.25) = 1.64872, f (0.5) = 2.71828, f (0.75) = 4.48169
b. f (0) if f (−0.5) = 1.93750, f (−0.25) = 1.33203, f (0.25) = 0.800781, f (0.5) = 0.687500
c. f (0.18) if f (0.1) = −0.29004986, f (0.2) = −0.56079734, f (0.3) = −0.81401972, f (0.4) = −1.0526302
d. f (0.25) if f (−1) = 0.86199480, f (−0.5) = 0.95802009, f (0) = 1.0986123, f (0.5) = 1.2943767
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