Example 4.  Use the function  [Graphics:Images/TangentParabolaMod_gr_225.gif]  and the point  [Graphics:Images/TangentParabolaMod_gr_226.gif]  and plot a sequence of Newton cubic polynomials converging to the Taylor polynomial.  

Solution 4.

[Graphics:../Images/TangentParabolaMod_gr_227.gif]

[Graphics:../Images/TangentParabolaMod_gr_228.gif]

 

 

 

[Graphics:../Images/TangentParabolaMod_gr_229.gif]

[Graphics:../Images/TangentParabolaMod_gr_230.gif]

[Graphics:../Images/TangentParabolaMod_gr_231.gif]

[Graphics:../Images/TangentParabolaMod_gr_232.gif]

[Graphics:../Images/TangentParabolaMod_gr_233.gif]

[Graphics:../Images/TangentParabolaMod_gr_234.gif]

[Graphics:../Images/TangentParabolaMod_gr_235.gif]

[Graphics:../Images/TangentParabolaMod_gr_236.gif]

[Graphics:../Images/TangentParabolaMod_gr_237.gif]

[Graphics:../Images/TangentParabolaMod_gr_238.gif]

[Graphics:../Images/TangentParabolaMod_gr_239.gif]

[Graphics:../Images/TangentParabolaMod_gr_240.gif]

[Graphics:../Images/TangentParabolaMod_gr_241.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004