Example 6. NON Convergence, Cycling  Find the solution to  [Graphics:Images/Newton'sMethodMod_gr_454.gif].  Use the starting approximation  [Graphics:Images/Newton'sMethodMod_gr_455.gif].  

Solution 6.

[Graphics:../Images/Newton'sMethodMod_gr_456.gif]

[Graphics:../Images/Newton'sMethodMod_gr_457.gif]

[Graphics:../Images/Newton'sMethodMod_gr_458.gif]
[Graphics:../Images/Newton'sMethodMod_gr_459.gif]
[Graphics:../Images/Newton'sMethodMod_gr_460.gif]

[Graphics:../Images/Newton'sMethodMod_gr_461.gif]
[Graphics:../Images/Newton'sMethodMod_gr_462.gif]
[Graphics:../Images/Newton'sMethodMod_gr_463.gif]
[Graphics:../Images/Newton'sMethodMod_gr_464.gif]
[Graphics:../Images/Newton'sMethodMod_gr_465.gif]
[Graphics:../Images/Newton'sMethodMod_gr_466.gif]
[Graphics:../Images/Newton'sMethodMod_gr_467.gif]
[Graphics:../Images/Newton'sMethodMod_gr_468.gif]
[Graphics:../Images/Newton'sMethodMod_gr_469.gif]
[Graphics:../Images/Newton'sMethodMod_gr_470.gif]
[Graphics:../Images/Newton'sMethodMod_gr_471.gif]
[Graphics:../Images/Newton'sMethodMod_gr_472.gif]
[Graphics:../Images/Newton'sMethodMod_gr_473.gif]
[Graphics:../Images/Newton'sMethodMod_gr_474.gif]
[Graphics:../Images/Newton'sMethodMod_gr_475.gif]
[Graphics:../Images/Newton'sMethodMod_gr_476.gif]
[Graphics:../Images/Newton'sMethodMod_gr_477.gif]
[Graphics:../Images/Newton'sMethodMod_gr_478.gif]
[Graphics:../Images/Newton'sMethodMod_gr_479.gif]
[Graphics:../Images/Newton'sMethodMod_gr_480.gif]
[Graphics:../Images/Newton'sMethodMod_gr_481.gif]
[Graphics:../Images/Newton'sMethodMod_gr_482.gif]

[Graphics:../Images/Newton'sMethodMod_gr_483.gif]

Animation 4.  ( Newton's Method Newton's Method ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004