Solution 17 (a).

See text and/or instructor's solution manual.

Solution.  By definition,   [Graphics:../Images/TaylorSeriesModHome_gr_845.gif],   so using the chain rule, we see that

                     [Graphics:../Images/TaylorSeriesModHome_gr_846.gif]  
                     
Hence we see that    [Graphics:../Images/TaylorSeriesModHome_gr_847.gif].

But, by definition, this means that  [Graphics:../Images/TaylorSeriesModHome_gr_848.gif]  is an even function.

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell