Example 9.  Given  [Graphics:Images/NumericalDiffMod_gr_220.gif], find numerical approximations to the derivative  [Graphics:Images/NumericalDiffMod_gr_221.gif], using two points and the forward difference formula.

Solution 9.

[Graphics:../Images/NumericalDiffMod_gr_222.gif]

[Graphics:../Images/NumericalDiffMod_gr_223.gif]

[Graphics:../Images/NumericalDiffMod_gr_224.gif]
[Graphics:../Images/NumericalDiffMod_gr_225.gif]

[Graphics:../Images/NumericalDiffMod_gr_226.gif]

[Graphics:../Images/NumericalDiffMod_gr_227.gif]
[Graphics:../Images/NumericalDiffMod_gr_228.gif]

[Graphics:../Images/NumericalDiffMod_gr_229.gif]

[Graphics:../Images/NumericalDiffMod_gr_230.gif]
[Graphics:../Images/NumericalDiffMod_gr_231.gif]

[Graphics:../Images/NumericalDiffMod_gr_232.gif]

[Graphics:../Images/NumericalDiffMod_gr_233.gif]
[Graphics:../Images/NumericalDiffMod_gr_234.gif]

[Graphics:../Images/NumericalDiffMod_gr_235.gif]

[Graphics:../Images/NumericalDiffMod_gr_236.gif]
[Graphics:../Images/NumericalDiffMod_gr_237.gif]

[Graphics:../Images/NumericalDiffMod_gr_238.gif]

[Graphics:../Images/NumericalDiffMod_gr_239.gif]
[Graphics:../Images/NumericalDiffMod_gr_240.gif]

Animation 1.  ( Numerical Differentiation  Numerical Differentiation ).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004