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158 Derivative Essay

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Kyle D. Antonio
2012-53215

A. Data analysis
First derivative (two-point formula)
x
h=0.1
h=0.01
h=0.001
h=0.0001
Exact value
1
2.858842
2.731919
2.719641
2.718418
2.718282
5
156.087479
149.157700
148.487396
148.420578
148.413162
10
23165.435547
22136.966797
22037.82422
22027.566406
22026.465795
20
510252704
487599136
485407872
485189440
485165184

The values of the derivative of ex are closer to the exact value when the value 0f h decreases. But it can also be seen that the percentage error of all value of x would yield almost the same value. As computed by the program when x=1, the PE=5.170916 and for x=20, the PE=5.170921. First derivative (three-point formula)

x
h=0.1
h=0.01
h=0.001...

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Keywords

-0.280862697 -1.043870004 -1.286433861 -1.348692905 -10 -2.057694247 -2.299555899 -2.321026624 -2.7780644 -2.969805215 -3 -3.078833949 -3.15490196 -3.301029996 -3.71219827 -3.928117993 -3.974694135 -4.301029996 -4.37675071 -4.769551079 -5 -5.096910013 -5.15490196 -5.301029996 -5.522878745 -53215 -6 /exact 0.000000 0.0000001 0.000001 0.00001 0.000013 0.0001 0.000136 0.001 0.001359 0.01 0.013637 0.1 0.14056 0.166750 0f 1 1.744165415 10 10.1987303 12.13534964 13.53430315 148.413162 148.413177 148.414398 148.415634 148.420578 148.487396 148.536880 148.660645 149.157700 156.087479 158 1e-07 1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14 1e-15 1x10 2.718282 2.718304 2.718327 2.718418 2.719641 2.720548 2.722815 2.731919 2.858842 20 2012 22026.465795 22026.466797 22026.468750 22026.648438 22026.832031 22027.566406 22037.82422 22044.828125 22063.195313 22136.966797 23165.435547 3.788970893 4.958745958 485165184 485165248 485165280 485169248 485173280 485189440 485407872 485569632 485974208 487599136 5 5.170916 5.170921 510252704 7.851235887 add almost also analysi antonio approxim b behavior better blank box calcul certain closer come compar comput conclud could d data decreas deriv equal error ex ex-exc exact excal exp f first formula graph greater h increas indic infer kyle linear log lower mean note pe percentag point precis previous produc program rang result second seen show tabl therefor three three-point thus two two-point use valu vs would x yield zero δ δe