Barrons AP Calculus

(c)

(a)

(b)

(c)

(a)

(b)

Figure  N10–3b

To  four    decimal places,  .  Evaluating  the polynomials at   ,  we  get 

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

Example 46 __

Find    the Taylor  polynomials of  degrees 0,  1,  2,  and 3   generated   by  f(x)    =   ln  x

at  x   =   1.

Graph   f   and the four    polynomials on  the same    set of  axes.

Using   P 2 ,   approximate ln  1.3,    and find    a   bound   on  the error.

BC  ONLY

SOLUTIONS:

The  derivatives     of  ln  x   at  x   =   1   are     given   in  the     table: 

From    the table   we  have

Figure   N10–4   shows   the     graphs  of  ln x    and     the     four    Taylor  polynomials