Example 4. Slow Convergence  Find the solution to  [Graphics:Images/Newton'sMethodMod_gr_394.gif].  Use the starting approximation  [Graphics:Images/Newton'sMethodMod_gr_395.gif].  

Solution 4.

[Graphics:../Images/Newton'sMethodMod_gr_396.gif]

[Graphics:../Images/Newton'sMethodMod_gr_397.gif]

[Graphics:../Images/Newton'sMethodMod_gr_398.gif]
[Graphics:../Images/Newton'sMethodMod_gr_399.gif]
[Graphics:../Images/Newton'sMethodMod_gr_400.gif]

[Graphics:../Images/Newton'sMethodMod_gr_401.gif]
[Graphics:../Images/Newton'sMethodMod_gr_402.gif]
[Graphics:../Images/Newton'sMethodMod_gr_403.gif]
[Graphics:../Images/Newton'sMethodMod_gr_404.gif]
[Graphics:../Images/Newton'sMethodMod_gr_405.gif]
[Graphics:../Images/Newton'sMethodMod_gr_406.gif]
[Graphics:../Images/Newton'sMethodMod_gr_407.gif]
[Graphics:../Images/Newton'sMethodMod_gr_408.gif]
[Graphics:../Images/Newton'sMethodMod_gr_409.gif]
[Graphics:../Images/Newton'sMethodMod_gr_410.gif]
[Graphics:../Images/Newton'sMethodMod_gr_411.gif]
[Graphics:../Images/Newton'sMethodMod_gr_412.gif]
[Graphics:../Images/Newton'sMethodMod_gr_413.gif]
[Graphics:../Images/Newton'sMethodMod_gr_414.gif]
[Graphics:../Images/Newton'sMethodMod_gr_415.gif]
[Graphics:../Images/Newton'sMethodMod_gr_416.gif]
[Graphics:../Images/Newton'sMethodMod_gr_417.gif]
[Graphics:../Images/Newton'sMethodMod_gr_418.gif]
[Graphics:../Images/Newton'sMethodMod_gr_419.gif]
[Graphics:../Images/Newton'sMethodMod_gr_420.gif]
[Graphics:../Images/Newton'sMethodMod_gr_421.gif]
[Graphics:../Images/Newton'sMethodMod_gr_422.gif]
[Graphics:../Images/Newton'sMethodMod_gr_423.gif]
[Graphics:../Images/Newton'sMethodMod_gr_424.gif]
[Graphics:../Images/Newton'sMethodMod_gr_425.gif]
[Graphics:../Images/Newton'sMethodMod_gr_426.gif]
[Graphics:../Images/Newton'sMethodMod_gr_427.gif]
[Graphics:../Images/Newton'sMethodMod_gr_428.gif]
[Graphics:../Images/Newton'sMethodMod_gr_429.gif]
[Graphics:../Images/Newton'sMethodMod_gr_430.gif]
[Graphics:../Images/Newton'sMethodMod_gr_431.gif]

[Graphics:../Images/Newton'sMethodMod_gr_432.gif]

Animation 2.  ( Newton's Method  Newton's Method ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004