Example 5. Convergence, Oscillation  Find the solution to  [Graphics:Images/Newton'sMethodMod_gr_433.gif].  Use the starting approximation  [Graphics:Images/Newton'sMethodMod_gr_434.gif].  

Solution 5.

[Graphics:../Images/Newton'sMethodMod_gr_435.gif]

[Graphics:../Images/Newton'sMethodMod_gr_436.gif]

[Graphics:../Images/Newton'sMethodMod_gr_437.gif]
[Graphics:../Images/Newton'sMethodMod_gr_438.gif]
[Graphics:../Images/Newton'sMethodMod_gr_439.gif]

[Graphics:../Images/Newton'sMethodMod_gr_440.gif]
[Graphics:../Images/Newton'sMethodMod_gr_441.gif]
[Graphics:../Images/Newton'sMethodMod_gr_442.gif]
[Graphics:../Images/Newton'sMethodMod_gr_443.gif]
[Graphics:../Images/Newton'sMethodMod_gr_444.gif]
[Graphics:../Images/Newton'sMethodMod_gr_445.gif]
[Graphics:../Images/Newton'sMethodMod_gr_446.gif]
[Graphics:../Images/Newton'sMethodMod_gr_447.gif]
[Graphics:../Images/Newton'sMethodMod_gr_448.gif]
[Graphics:../Images/Newton'sMethodMod_gr_449.gif]
[Graphics:../Images/Newton'sMethodMod_gr_450.gif]
[Graphics:../Images/Newton'sMethodMod_gr_451.gif]
[Graphics:../Images/Newton'sMethodMod_gr_452.gif]

[Graphics:../Images/Newton'sMethodMod_gr_453.gif]

Animation 3.  ( Newton's Method  Newton's Method ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004