Example 3. Fast Convergence  Find the solution to  [Graphics:Images/Newton'sMethodMod_gr_374.gif].  Use the starting approximation  [Graphics:Images/Newton'sMethodMod_gr_375.gif].  

Solution 3.

[Graphics:../Images/Newton'sMethodMod_gr_376.gif]


[Graphics:../Images/Newton'sMethodMod_gr_377.gif]

[Graphics:../Images/Newton'sMethodMod_gr_378.gif]
[Graphics:../Images/Newton'sMethodMod_gr_379.gif]
[Graphics:../Images/Newton'sMethodMod_gr_380.gif]

[Graphics:../Images/Newton'sMethodMod_gr_381.gif]
[Graphics:../Images/Newton'sMethodMod_gr_382.gif]
[Graphics:../Images/Newton'sMethodMod_gr_383.gif]
[Graphics:../Images/Newton'sMethodMod_gr_384.gif]
[Graphics:../Images/Newton'sMethodMod_gr_385.gif]
[Graphics:../Images/Newton'sMethodMod_gr_386.gif]
[Graphics:../Images/Newton'sMethodMod_gr_387.gif]
[Graphics:../Images/Newton'sMethodMod_gr_388.gif]
[Graphics:../Images/Newton'sMethodMod_gr_389.gif]
[Graphics:../Images/Newton'sMethodMod_gr_390.gif]
[Graphics:../Images/Newton'sMethodMod_gr_391.gif]
[Graphics:../Images/Newton'sMethodMod_gr_392.gif]

[Graphics:../Images/Newton'sMethodMod_gr_393.gif]

Animation 1.  ( Newton's Method  Newton's Method ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004