Estudo Dirigido Métodos Numéricos e Computacionais

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

Calculo de área
	integração numerica
	limite inferior (xi)	-2
	Limite superior(xf)	2	Ao realizar a terraplanagem de uma obra localizada em Paranaguá, um engenheiro se depara com um aterro que precisa ser feito, o buraco tem 6 metros de profundidade e seu formato pode ser compreendido por f(x)=4-X^2, qual o volume de terra necessário para aterrar este buraco?
	Numero de intervalos(n)	200
	Delta x	0.02
	i	xmi	f(xmi)	|f(xmi)|	|f(xmi)|^2
	1	-1.99	0.04	0.0399	0.00159201
	2	-1.97	0.12	0.1191	0.01418481	Área=	10.67	m^2
	3	-1.95	0.20	0.1975	0.03900625
	4	-1.93	0.28	0.2751	0.07568001	Area do buraco*Altura do buraco=Volume de terra necessário
	5	-1.91	0.35	0.3519	0.12383361
	6	-1.89	0.43	0.4279	0.18309841	Volume necessário=	64.0008	m^3
	7	-1.87	0.50	0.5031	0.25310961
	8	-1.85	0.58	0.5775	0.33350625
	9	-1.83	0.65	0.6511	0.42393121
	10	-1.81	0.72	0.7239	0.52403121
	11	-1.79	0.80	0.7959	0.63345681
	12	-1.77	0.87	0.8671	0.75186241
	13	-1.75	0.94	0.9375	0.87890625
	14	-1.73	1.01	1.0071	1.01425041
	15	-1.71	1.08	1.0759	1.15756081
	16	-1.69	1.14	1.1439	1.30850721
	17	-1.67	1.21	1.2111	1.46676321
	18	-1.65	1.28	1.2775	1.63200625
	19	-1.63	1.34	1.3431	1.80391761
	20	-1.61	1.41	1.4079	1.98218241
	21	-1.59	1.47	1.4719	2.16648961
	22	-1.57	1.54	1.5351	2.35653201
	23	-1.55	1.60	1.5975	2.55200625
	24	-1.53	1.66	1.6591	2.75261281
	25	-1.51	1.72	1.7199	2.95805601
	26	-1.49	1.78	1.7799	3.16804401
	27	-1.47	1.84	1.8391	3.38228881
	28	-1.45	1.90	1.8975	3.60050625
	29	-1.43	1.96	1.9551	3.82241601
	30	-1.41	2.01	2.0119	4.04774161
	31	-1.39	2.07	2.0679	4.27621041
	32	-1.37	2.12	2.1231	4.50755361
	33	-1.35	2.18	2.1775	4.74150625
	34	-1.33	2.23	2.2311	4.97780721
	35	-1.31	2.28	2.2839	5.21619921
	36	-1.29	2.34	2.3359	5.45642881
	37	-1.27	2.39	2.3871	5.69824641
	38	-1.25	2.44	2.4375	5.94140625
	39	-1.23	2.49	2.4871	6.18566641
	40	-1.21	2.54	2.5359	6.43078881
	41	-1.19	2.58	2.5839	6.67653921
	42	-1.17	2.63	2.6311	6.92268721
	43	-1.15	2.68	2.6775	7.16900625
	44	-1.13	2.72	2.7231	7.41527361
	45	-1.11	2.77	2.7679	7.66127041
	46	-1.09	2.81	2.8119	7.90678161
	47	-1.07	2.86	2.8551	8.15159601
	48	-1.05	2.90	2.8975	8.39550625
	49	-1.03	2.94	2.9391	8.63830881
	50	-1.01	2.98	2.9799	8.87980401
	51	-0.99	3.02	3.0199	9.11979601
	52	-0.97	3.06	3.0591	9.35809281
	53	-0.95	3.10	3.0975	9.59450625
	54	-0.93	3.14	3.1351	9.82885201
	55	-0.91	3.17	3.1719	10.06094961
	56	-0.89	3.21	3.2079	10.29062241
	57	-0.87	3.24	3.2431	10.51769761
	58	-0.85	3.28	3.2775	10.74200625
	59	-0.83	3.31	3.3111	10.96338321
	60	-0.81	3.34	3.3439	11.18166721
	61	-0.79	3.38	3.3759	11.39670081
	62	-0.77	3.41	3.4071	11.60833041
	63	-0.75	3.44	3.4375	11.81640625
	64	-0.73	3.47	3.4671	12.02078241
	65	-0.71	3.50	3.4959	12.22131681
	66	-0.69	3.52	3.5239	12.41787121
	67	-0.67	3.55	3.5511	12.61031121
	68	-0.65	3.58	3.5775	12.79850625
	69	-0.63	3.60	3.6031	12.98232961
	70	-0.61	3.63	3.6279	13.16165841
	71	-0.59	3.65	3.6519	13.33637361
	72	-0.57	3.68	3.6751	13.50636001
	73	-0.55	3.70	3.6975	13.67150625
	74	-0.53	3.72	3.7191	13.83170481
	75	-0.51	3.74	3.7399	13.98685201
	76	-0.49	3.76	3.7599	14.13684801
	77	-0.47	3.78	3.7791	14.28159681
	78	-0.45	3.80	3.7975	14.42100625
	79	-0.43	3.82	3.8151	14.55498801
	80	-0.41	3.83	3.8319	14.68345761
	81	-0.39	3.85	3.8479	14.80633441
	82	-0.37	3.86	3.8631	14.92354161
	83	-0.35	3.88	3.8775	15.03500625
	84	-0.33	3.89	3.8911	15.14065921
	85	-0.31	3.90	3.9039	15.24043521
	86	-0.29	3.92	3.9159	15.33427281
	87	-0.27	3.93	3.9271	15.42211441
	88	-0.25	3.94	3.9375	15.50390625
	89	-0.23	3.95	3.9471	15.57959841
	90	-0.21	3.96	3.9559	15.64914481
	91	-0.19	3.96	3.9639	15.71250321
	92	-0.17	3.97	3.9711	15.76963521
	93	-0.15	3.98	3.9775	15.82050625
	94	-0.13	3.98	3.9831	15.86508561
	95	-0.11	3.99	3.9879	15.90334641
	96	-0.09	3.99	3.9919	15.93526561
	97	-0.07	4.00	3.9951	15.96082401
	98	-0.05	4.00	3.9975	15.98000625
	99	-0.03	4.00	3.9991	15.99280081
	100	-0.01	4.00	3.9999	15.99920001
	101	0.01	4.00	3.9999	15.99920001
	102	0.03	4.00	3.9991	15.99280081
	103	0.05	4.00	3.9975	15.98000625
	104	0.07	4.00	3.9951	15.96082401
	105	0.09	3.99	3.9919	15.93526561
	106	0.11	3.99	3.9879	15.90334641
	107	0.13	3.98	3.9831	15.86508561
	108	0.15	3.98	3.9775	15.82050625
	109	0.17	3.97	3.9711	15.76963521
	110	0.19	3.96	3.9639	15.71250321
	111	0.21	3.96	3.9559	15.64914481
	112	0.23	3.95	3.9471	15.57959841
	113	0.25	3.94	3.9375	15.50390625
	114	0.27	3.93	3.9271	15.42211441
	115	0.29	3.92	3.9159	15.33427281
	116	0.31	3.90	3.9039	15.24043521
	117	0.33	3.89	3.8911	15.14065921
	118	0.35	3.88	3.8775	15.03500625
	119	0.37	3.86	3.8631	14.92354161
	120	0.39	3.85	3.8479	14.80633441
	121	0.41	3.83	3.8319	14.68345761
	122	0.43	3.82	3.8151	14.55498801
	123	0.45	3.80	3.7975	14.42100625
	124	0.47	3.78	3.7791	14.28159681
	125	0.49	3.76	3.7599	14.13684801
	126	0.51	3.74	3.7399	13.98685201
	127	0.53	3.72	3.7191	13.83170481
	128	0.55	3.70	3.6975	13.67150625
	129	0.57	3.68	3.6751	13.50636001
	130	0.59	3.65	3.6519	13.33637361
	131	0.61	3.63	3.6279	13.16165841
	132	0.63	3.60	3.6031	12.98232961
	133	0.65	3.58	3.5775	12.79850625
	134	0.67	3.55	3.5511	12.61031121
	135	0.69	3.52	3.5239	12.41787121
	136	0.71	3.50	3.4959	12.22131681
	137	0.73	3.47	3.4671	12.02078241
	138	0.75	3.44	3.4375	11.81640625
	139	0.77	3.41	3.4071	11.60833041
	140	0.79	3.38	3.3759	11.39670081
	141	0.81	3.34	3.3439	11.18166721
	142	0.83	3.31	3.3111	10.96338321
	143	0.85	3.28	3.2775	10.74200625
	144	0.87	3.24	3.2431	10.51769761
	145	0.89	3.21	3.2079	10.29062241
	146	0.91	3.17	3.1719	10.06094961
	147	0.93	3.14	3.1351	9.82885201
	148	0.95	3.10	3.0975	9.59450625
	149	0.97	3.06	3.0591	9.35809281
	150	0.99	3.02	3.0199	9.11979601
	151	1.01	2.98	2.9799	8.87980401
	152	1.03	2.94	2.9391	8.63830881
	153	1.05	2.90	2.8975	8.39550625
	154	1.07	2.86	2.8551	8.15159601
	155	1.09	2.81	2.8119	7.90678161
	156	1.11	2.77	2.7679	7.66127041
	157	1.13	2.72	2.7231	7.41527361
	158	1.15	2.68	2.6775	7.16900625
	159	1.17	2.63	2.6311	6.92268721
	160	1.19	2.58	2.5839	6.67653921
	161	1.21	2.54	2.5359	6.43078881
	162	1.23	2.49	2.4871	6.18566641
	163	1.25	2.44	2.4375	5.94140625
	164	1.27	2.39	2.3871	5.69824641
	165	1.29	2.34	2.3359	5.45642881
	166	1.31	2.28	2.2839	5.21619921
	167	1.33	2.23	2.2311	4.97780721
	168	1.35	2.18	2.1775	4.74150625
	169	1.37	2.12	2.1231	4.50755361
	170	1.39	2.07	2.0679	4.27621041
	171	1.41	2.01	2.0119	4.04774161
	172	1.43	1.96	1.9551	3.82241601
	173	1.45	1.90	1.8975	3.60050625
	174	1.47	1.84	1.8391	3.38228881
	175	1.49	1.78	1.7799	3.16804401
	176	1.51	1.72	1.7199	2.95805601
	177	1.53	1.66	1.6591	2.75261281
	178	1.55	1.60	1.5975	2.55200625
	179	1.57	1.54	1.5351	2.35653201
	180	1.59	1.47	1.4719	2.16648961
	181	1.61	1.41	1.4079	1.98218241
	182	1.63	1.34	1.3431	1.80391761
	183	1.65	1.28	1.2775	1.63200625
	184	1.67	1.21	1.2111	1.46676321
	185	1.69	1.14	1.1439	1.30850721
	186	1.71	1.08	1.0759	1.15756081
	187	1.73	1.01	1.0071	1.01425041
	188	1.75	0.94	0.9375	0.87890625
	189	1.77	0.87	0.8671	0.75186241
	190	1.79	0.80	0.7959	0.63345681
	191	1.81	0.72	0.7239	0.52403121
	192	1.83	0.65	0.6511	0.42393121
	193	1.85	0.58	0.5775	0.33350625
	194	1.87	0.50	0.5031	0.25310961
	195	1.89	0.43	0.4279	0.18309841
	196	1.91	0.35	0.3519	0.12383361
	197	1.93	0.28	0.2751	0.07568001
	198	1.95	0.20	0.1975	0.03900625
	199	1.97	0.12	0.1191	0.01418481
	200	1.99	0.04	0.0399	0.00159201
Otimização
	
Para a redução de gastos na construção de uma caixa d’água de uma empresa, o proprietário contrata um engenheiro para que calcule as dimensões mínimas a serem usadas para uma caixa d’água de 20.000 litros.Quais são as dimensões mínimas para construção?
	1E-3
	x	x+Delta x	x-Delta x	f(x)	f(x+Delta x)	f(x-Delta x)	f'(x)	f''(x)	Furmula usada:
	14.7101291478	14.7111291478	14.7091291478	4078.8200106643	4078.8200292277	4078.8200298001	-0	37.6991511075
	r=	14.71	(usado "atingir metas")
	h=	29.42