Solution 10.

See text and/or instructor's solution manual.

Solution.   Start with

                    [Graphics:../Images/TaylorSeriesModHome_gr_684.gif].  

Use Corollary 4.3, which states that if  [Graphics:../Images/TaylorSeriesModHome_gr_685.gif]  then  

                    [Graphics:../Images/TaylorSeriesModHome_gr_686.gif].  

Make the substitution  [Graphics:../Images/TaylorSeriesModHome_gr_687.gif]  and  get  

                    [Graphics:../Images/TaylorSeriesModHome_gr_688.gif]     


Therefore,   [Graphics:../Images/TaylorSeriesModHome_gr_689.gif]where  [Graphics:../Images/TaylorSeriesModHome_gr_690.gif],  and  n  is a positive integer.     

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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