Example 5.  Consider the function  .  
5 (c).  Find the terms up to    in the Maclaurin series and see how close it approximates  f[x].
Solution 5 (c).

5 (c).  Find the terms up to    in the Maclaurin series and see how close it approximates  f[x].

Go ahead "enjoy" and add terms in the series up to , then plot the functions over the interval [-3.0, 3.0].

Question.  Do we have a "good approximation" on the interval  [-3.0, 3.0] ?

Aside.  Mathematica actually computes the higher derivatives of f[x] up to the order 50 when calculating the Taylor series. Suppose you had to find the formula for the first 20 derivatives of f[x].  Could "you" do it ?  Would you want to do it ?

(c) John H. Mathews 2004