We estimate integrals using Taylor polynomials. Exercise 72 is used to estimate the error. Let T 4 be the fourth Maclaurin polynomial for (x) =

We estimate integrals using Taylor polynomials. Exercise 72 is used to estimate the error.

Let T₄ be the fourth Maclaurin polynomial for ƒ(x) = cos x.
(a) Show that

T₄(x) = T₅(x).

Data From Exercise 72

Let L > 0. Show that if two functions ƒ and g satisfy |ƒ(x) − g(x)|

| cos x - T4(x)| 12 6! [0,1/1 for all x 0, xe