Resoluções AP2 - Calc_Num

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Sheet1
	Interpolação forma de Lagrange
	n	xn	yn	Ln	(x-xn)	xn-xk
	1	1	0.346	-0.125	-1.5	0	1	2
	2	2	0.975	0.75	-0.5	-1	0	1
	3	3	0.144	0.375	0.5	-2	-1	0
	4				2.5	1	0.975	0.975
	5				2.5	1	0.975	0.975
	6				2.5	1	0.975	0.975
	7				2.5	1	0.975	0.975
	8				2.5	1	0.975	0.975
	9				2.5	1	0.975	0.975
	x	2.5	0.742
	s1	-0.04325
	s1	0.73125
	s1	0.054
	s1	0
	s1	0
	s1	0
	s1	0
	s1	0
	s1	0
	s1	0
	Interpolação forma de Newton
	n	xn	yn	En	(x-xn)	(x1-xn)	(x2-xn)	(x3-xn)	f[xn]	f(x1)-f(xn)	f(x2)-f(xn)	f(x3)-f(xn)	f[x1,x2]	f[x1,x3]	f[x3,x2]	f[x1,x]	f[x1,x2,x3]	f[x1,x2,x]	f[x1,x2,x3,x]
	1	1	-1.247		0.5	0	1	2	-1.247	0	21.348	55.69	21.348	27.845	34.342	18.0995	6.497	6.497	0
	2	2	20.101		-0.5	-1	0	1	20.101	-21.348	0	34.342
	3	3	54.443		-1.5	-2	-1	0	54.443	-55.69	-34.342	0
	x	1.5	7.80275		0	-0.5	0.5	1.5	7.80275	-9.04975	12.29825	46.64025	ERROR:#DIV/0!	ERROR:#DIV/0!	ERROR:#DIV/0!		ERROR:#DIV/0!
	s1	0
	s1	0
	s1	0
	s1	ERROR:#REF!
	s1	0
	s1	0
	s1	0
	s1	0
	s1	0
	s1	0
	Quadratura de Gauss
	a	b	x	t	f(x)	na	nb	x(t)	f(t)
	0	1				1	-1	0.5	0.3121660893
	0.5773502692	-0.5773502692
	Regra dos trapézios Generalizada
	12.7729932856	6.3594072272	25.5730759867
	0	2	3.1378581622	3.1553886402
	1	2.8	3.1729191182	3.1829158116
	2	3.6	3.1929125051	3.1993733015
	3	4.4	3.2058340978	3.210353185
	4	5.2	3.2148722722	3.2182106686
	5	6	3.221549065
				15.966241607
	Regra de 1/3 de Simpson
	4.4889314337
		0	0.8198276498
		1.5	1.4442334099
		3	2.381101578
	Regra do trapézio
		2.9765285888	2.4142135624	2.2360679775
		0	1	1	1.0590169944
		0.5	1.1180339887	1.1180339887	1.2661237756
		1	1.4142135624	1.4142135624	1.6084946001
		1.5	1.8027756377	1.8027756377	2.0194218076
		2	2.2360679775	2.2360679775
	7, Euler no PVI
	f(x,y)	x	y
		0	2
	-4	1	-2
	-6	2	-8
	9, euler aperfeiçoado
	f(t,y)	t	y
		1	2
	3	2	5.25
	3.625	3	9.4166666667
	10, trapézios generalizada
	t	0	5	10	15	20	25	30	35	40
	a(t)	40	45.25	48.5	51.25	54.35	59.48	61.5	64.3	68.7
	2at		90.5	97	102.5	108.7	118.96	123	128.6	137.4
	t0
	v(t0)	2194.9	438.98
		2194.9
			42.625	46.875	49.875	52.8	56.915	60.49	62.9	66.5
		30	35.25	38.5	41.25	44.35	49.48	51.5	54.3	58.7
			32.625	36.875	39.875	42.8	46.915	50.49	52.9	56.5
		1794.9