Let f ∈ C[a, b] be a function whose derivative exists on (a, b). Suppose f is to be evaluated at x0 in (a, b), but instead of computing the actual value f (x0), the approximate value,  (x0), is the actual value of f at x0 + , that is,  (x0) = f (x0 + ().
a. Use the Mean Value Theorem 1.8 to estimate the absolute error |f (x0) −  (x0)| and the relative error |f (x0) −  (x0)|/|f (x0)|, assuming f (x0) ≠ 0.
b. If ( = 5 × 10−6 and x0 = 1, find bounds for the absolute and relative errors for
i. f (x) = ex
ii. f (x) = sin x
c. Repeat part (b) with ( = (5 × 10−6)x0 and x0 = 10.