Taylor_Series_Approx_Examples_01.xls

	A	B	C	D	E	F	G
1	Solved example: Taylor series approximation for the function f(x) = e-x (for xi = 0.2, xi+1 = 1)
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3		xi	0.2
4		xi+1	1
5		Δx = xi+1 - xi	0.8
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8			True value	True value	Approx value (Calculated using Taylor Series)	True percent relative error	Log of true percent relative error
9			f(xi)	f(xi+1)	f(xi+1)	\|εt\|	log(\|εt\|)
10	0	0th order approx	0.818731	0.367879	0.818731	122.554	2.088
11	1	1st order approx	0.818731	0.367879	0.163746	55.489	1.744
12	2	2nd order approx	0.818731	0.367879	0.425740	15.728	1.197
13	3	3rd order approx	0.818731	0.367879	0.355875	3.263	0.514
14	4	4th order approx	0.818731	0.367879	0.369848	0.535	-0.272
15	5	5th order approx	0.818731	0.367879	0.367612	0.073	-1.139
16	6	6th order approx	0.818731	0.367879	0.367910	8.41E-03	-2.075
17	7	7th order approx	0.818731	0.367879	0.367876	8.50E-04	-3.071
18	8	8th order approx	0.818731	0.367879	0.367880	7.62E-05	-4.118
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