Barrons AP Calculus

(c)

above,  in  [0,2.5] ×   [−1,1].

Figure  N10–4

ln  .

For x   =   1.3 the Taylor  series  converges   by  the Alternating Series  Test,   so  the

error   is  less    than    the magnitude   of  the first   omitted term:   

BC  ONLY

Example 47 __

For what positive values of x is the approximate formula

correct to three decimal places?

SOLUTION: We can use series (4):

For x > 0, this is an alternating series with terms decreasing in magnitude and