Extra Example 1.  Use the limit definition to find the derivative  [Graphics:Images/AnalyticFunctionMod_gr_13.gif].  

Explore Extra Example 1.

 

Method (i).

 

[Graphics:../Images/AnalyticFunctionMod_gr_14.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_15.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_16.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_17.gif]

Method (ii).

[Graphics:../Images/AnalyticFunctionMod_gr_18.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_19.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_20.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_21.gif]

 

Method (iii).

 


[Graphics:../Images/AnalyticFunctionMod_gr_22.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_23.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_24.gif]


[Graphics:../Images/AnalyticFunctionMod_gr_25.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell