Example 5.  Use the function  [Graphics:Images/TangentParabolaMod_gr_254.gif]  and the point  [Graphics:Images/TangentParabolaMod_gr_255.gif]  and plot a sequence of Newton polynomials of degree 6 converging to the Taylor polynomial.  

Solution 5.

[Graphics:../Images/TangentParabolaMod_gr_256.gif]

[Graphics:../Images/TangentParabolaMod_gr_257.gif]

 

 

 

[Graphics:../Images/TangentParabolaMod_gr_258.gif]

[Graphics:../Images/TangentParabolaMod_gr_259.gif]

[Graphics:../Images/TangentParabolaMod_gr_260.gif]

[Graphics:../Images/TangentParabolaMod_gr_261.gif]

[Graphics:../Images/TangentParabolaMod_gr_262.gif]

[Graphics:../Images/TangentParabolaMod_gr_263.gif]

[Graphics:../Images/TangentParabolaMod_gr_264.gif]

[Graphics:../Images/TangentParabolaMod_gr_265.gif]

[Graphics:../Images/TangentParabolaMod_gr_266.gif]

[Graphics:../Images/TangentParabolaMod_gr_267.gif]

[Graphics:../Images/TangentParabolaMod_gr_268.gif]

[Graphics:../Images/TangentParabolaMod_gr_269.gif]

[Graphics:../Images/TangentParabolaMod_gr_270.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004