Repeat Exercise 9 using x0 = π/6. Reference: Exercise 9 Find the second Taylor...

Repeat Exercise 9 using x₀ = π/6.

Reference: Exercise 9

Find the second Taylor polynomial P₂(x) for the function f (x) = e^x cos x about x₀ = 0.

a. Use P₂(0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) − P₂(0.5)| using the error formula, and compare it to the actual error.

b. Find a bound for the error |f (x) − P₂(x)| in using P₂(x) to approximate f (x) on the interval [0, 1].

c. Approximate

d. Find an upper bound for the error in (c) using and compare the bound to the actual error.