Barrons AP Calculus - David Bock

From the table we know that

(b) Figure N10–3a shows the graphs of sin x and the four polynomials. In Figure N10–3b we see

graphs only of sin x and P 7 (x), to exhibit how closely P 7 “follows” the sine curve.

FIGURE N10–3a

FIGURE N10–3b

(c) To four decimal places, sin = 0.8660. Evaluating the polynomials at we get

We see that P 7 is correct to four decimal places.

EXAMPLE 46
(a) Find the Taylor polynomials of degrees 0, 1, 2, and 3 generated by f (x) = ln x at x = 1.
(b) Graph f and the four polynomials on the same set of axes.
(c) Using P 2 , approximate ln 1.3, and find a bound on the error.