(Solution) - Use Theorem 3 3 to find an error bound for the -(2025 Original AI-Free Solution)

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Use Theorem 3.3 to find an error bound for the approximations in Exercise 2.
In Exercise 2
For the given functions f (x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f (1.4), and find the absolute error.
a. f (x) = sin ?x
b. f (x) = 3?(x - 1)
c. f (x) = log10(3x ? 1)
d. f (x) = e2x - x