Example 11.   Given  [Graphics:Images/NumericalDiffMod_gr_262.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_263.gif], using two points and the central difference formula.

Solution 11.

[Graphics:../Images/NumericalDiffMod_gr_264.gif]

[Graphics:../Images/NumericalDiffMod_gr_265.gif]

[Graphics:../Images/NumericalDiffMod_gr_266.gif]
[Graphics:../Images/NumericalDiffMod_gr_267.gif]

[Graphics:../Images/NumericalDiffMod_gr_268.gif]

[Graphics:../Images/NumericalDiffMod_gr_269.gif]
[Graphics:../Images/NumericalDiffMod_gr_270.gif]

[Graphics:../Images/NumericalDiffMod_gr_271.gif]

[Graphics:../Images/NumericalDiffMod_gr_272.gif]
[Graphics:../Images/NumericalDiffMod_gr_273.gif]

[Graphics:../Images/NumericalDiffMod_gr_274.gif]

[Graphics:../Images/NumericalDiffMod_gr_275.gif]
[Graphics:../Images/NumericalDiffMod_gr_276.gif]

[Graphics:../Images/NumericalDiffMod_gr_277.gif]

[Graphics:../Images/NumericalDiffMod_gr_278.gif]
[Graphics:../Images/NumericalDiffMod_gr_279.gif]

[Graphics:../Images/NumericalDiffMod_gr_280.gif]

[Graphics:../Images/NumericalDiffMod_gr_281.gif]
[Graphics:../Images/NumericalDiffMod_gr_282.gif]

Animation 6.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004