The data in Exercise 2 were generated using the following functions. Use the polynomials...

The data in Exercise 2 were generated using the following functions. Use the polynomials constructed in Exercise 2 for the given value of x to approximate f (x), and calculate the absolute error.

a. f ( x ) = e²x ; approximate f (0.43).

b. f ( x ) = x⁴ − x³ + x² − x + 1; approximate f (0).

c. f ( x ) = x² cos x − 3x; approximate f (0.18).

d. f ( x ) = ln(e^x + 2); approximate f (0.25).

Reference: Exercise 2

Use Theorem 3.9 or Algorithm 3.3 to construct an approximating polynomial for the following data.

Reference: Algorithm 3.3

Reference: Theorem 3.9