Zeros de Funções Reais

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Bissecção 
	a) f(x)= 1-xln(x), com Ɛ=10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	1	2	1.5	1	-0.3862943611	0.3918023378	1.5	1	1
	2	1.5	2	1.75	0.3918023378	-0.3862943611	0.0206723711	0.25	2	-0.3862943611
	3	1.75	2	1.875	0.0206723711	-0.3862943611	-0.1786412364	0.125	3	-2.295836866
	4	1.75	1.875	1.8125	0.0206723711	-0.1786412364	-0.0779066328	0.0625	4	-4.5451774445
	5	1.75	1.812	1.781	0.0206723711	-0.0771093482	-0.0279486827	0.0315	1.5	0.3918023378
	6	1.75	1.781	1.7655	0.0206723711	-0.0279486827	-0.0035701147	0.0155	1.8	-0.0580159968
	7	1.75	1.765	1.7575	0.0206723711	-0.0027859685	0.0089592042	0.008
	8	1.757	1.765	1.761	0.0097410792	-0.0027859685	0.0034820982	0.0035
	9	1.761	1.765	1.763	0.0034820982	-0.0027859685	0.0003491993	0.002
	10	1.763	1.765	1.764	0.0003491993	-0.0027859685	-0.0012181012	0.001
	11	1.763	1.764	1.7635	0.0003491993	-0.0012181012	-0.0004343801	0.0005
	12	1.763	1.764	1.7635	0.0003491993	-0.0012181012	-0.0004343801	0
	b) f(x)= 2^x-3x, com Ɛ=10^-2 (0,01)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	0	1	0.5	1	-1	-0.0857864376	0.5	-3	9.125
	2	0	0.5	0.25	1	-0.0857864376	0.439207115	0.5	-2	6.25
	3	0.25	0.5	0.375	0.439207115	-0.0857864376	0.1718395547	0.125	-1	3.5
	4	0.5	0.375	0.4375	-0.0857864376	0.1718395547	0.0417555469	0.0625	0	1
	5	0.5	0.4375	0.46875	-0.0857864376	0.0417555469	-0.022340118	0.0312	1	-1
	6	0.468	0.438	0.453	-0.020809371	0.0407249775	0.0098838131	0.015	2	-2
	7	0.468	0.453	0.4605	-0.020809371	0.0098838131	-0.0054813728	0.0075	3	-1
	8	0.46	0.453	0.4565	-0.0044581819	0.0098838131	0.0027087775	0.004	4	4
	9	0.46	0.4565	0.45825	-0.0044581819	0.0027087775	-0.0008757129	0.00175	5	17
	10	0.458	0.457	0.4575	-0.0003637666	0.0016844313	0.0006602499	0.00075	6	46
	11	0.458	0.457	0.4575	-0.0003637666	0.0016844313	0.0006602499	0	7	107
	c) f(x)= x^3+x-1000, com Ɛ=10^-5 (0,00001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	9	10	9.5	-262	10	-133.125	9.5	9	-262
	2	9.5	10	9.75	-133.125	10	-63.390625	0.25	10	10
	3	9.75	10	9.875	-63.390625	10	-27.158203125	0.125	-1000
	4	9.875	10	9.9375	-27.158203125	10	-8.6955566406	0.0625	-1000
	5	9.937	10	9.9685	-8.844180047	10	0.5482362441	0.031	-1000
	6	9.937	9.968	9.9525	-8.844180047	0.398687232	-4.2299196719	0.016	-1000
	7	9.952	9.968	9.96	-4.378990592	0.398687232	-1.992064	0.0075	-1000
	8	9.96	9.968	9.964	-1.992064	0.398687232	-0.797166656	0.004	-1000
	9	9.964	9.968	9.966	-0.797166656	0.398687232	-0.199359304	0.002	-1000
	10	9.966	9.968	9.967	-0.199359304	0.398687232	0.099634063	0.001	-1000
	11	9.966	9.967	9.9665	-0.199359304	0.099634063	-0.0498700954	0.0005	-1000
	12	9.966	9.967	9.9665	-0.199359304	0.099634063	-0.0498700954	0
	d) f(x)= x^3-2x^2-3x+10, com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	-3	-2	-2.5	-26	0	-10.625	2.5	-3	-26
	2	-2.5	-2	-2.25	-10.625	0	-4.765625	0.25	-2	0
	3	-2.25	-2	-2.125	-4.765625	0	-2.251953125	0.125	10
	4	-2.125	-2	-2.0625	-2.251953125	0	-1.0939941406	0.063	10
	5	-2.062	-2	-2.031	-1.084990328	0	-0.534717791	0.031	10
	6	-2.031	-2	-2.0155	-0.534717791	0	-0.2654257239	0.016	10
	7	-2.015	-2	-2.0075	-0.256803375	0	-0.1279504219	0.008	10
	8	-2.007	-2	-2.0035	-0.119392343	0	-0.0595980429	0.004	10
	9	-2.003	-2	-2.0015	-0.051072027	0	-0.0255180034	0.002	10
	10	-2.001	-2	-2.0005	-0.017008001	0	-0.0085020001	0.001	10
	11	-2	-2	-2	0	0	0	0	10
	e) f(x)= e^x-x-2, com Ɛ= 10^-4 (0,0001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	-2	-1	-1.5	0.1353633504	-0.6320824135	-0.2768351345	1.5	-3	1.0498025572
	2	-2	-1.5	-1.75	0.1353633504	-0.2768351345	-0.0761945228	0.25	-2	0.1353633504
	3	-2	-1.75	-1.875	0.1353633504	-0.0761945228	0.0283847832	0.125	-1	-0.6320824135
	4	-1.875	-1.75	-1.8125	0.0283847832	-0.0761945228	-0.0242238063	0.063	0	-1
	5	-1.875	-1.812	-1.8435	0.0283847832	-0.0246421563	0.0017927902	0.031	1	-0.282
	6	-1.843	-1.812	-1.8275	0.0013719482	-0.0246421563	-0.011654422	0.016	2	3.387524
	7	-1.843	-1.827	-1.835	0.0013719482	-0.0120739874	-0.0053561272	0.008	3	15.079290232
	8	-1.843	-1.835	-1.839	0.0013719482	-0.0053561272	-0.0019933613	0.004	4	48.5755108506
	9	-1.843	-1.839	-1.841	0.0013719482	-0.0019933613	-0.0003110238	0.002	5	141.3362384919
	10	-1.843	-1.841	-1.842	0.0013719482	-0.0003110238	0.0005303829	0.001	6	395.1778962209
	11	-1.842	-1.841	-1.8415	0.0005303829	-0.0003110238	0.0001096597	0.001	7	1086.8375219284
	12	-1.841	-1.841	-1.841	-0.0003110238	-0.0003110238	-0.0003110238	0
	f) f(x)= 70e^-1,5x+2,5e^-0,07x-9, com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	1	2	1.5	8.9525420514	-3.3403938598	0.630502929	1.5	0	63.3310014679
	2	1.5	2	1.75	0.630502929	-3.3403938598	-1.7160438437	0.25	1	8.7949677208
	3	1.5	1.75	1.625	0.630502929	-1.7160438437	-0.6506932016	0.125	2	-3.4873162582
	4	1.5	1.625	1.5625	0.630502929	-0.6506932016	-0.0396603805	0.063	3	-6.3324931233
	5	1.5	1.562	1.531	0.630502929	-0.034541088	0.2903599612	0.031	4	-7.0645952135
	6	1.531	1.562	1.5465	0.2903599612	-0.034541088	0.1260482005	0.015	5	-7.3185653929
	7	1.546	1.562	1.554	0.1312900122	-0.034541088	0.0478842074	0.008	6	-7.4597094496
	8	1.554	1.562	1.558	0.0478842074	-0.034541088	0.0065497297	0.004	7	-7.5699647713
	9	1.558	1.562	1.56	0.0065497297	-0.034541088	-0.0140260454	0.002	8	-7.6680028906
	10	1.558	1.56	1.559	0.0065497297	-0.0140260454	-0.0037457608	0.001	9	-7.7583505315
	11	1.558	1.559	1.5585	0.0065497297	-0.0037457608	0.0014000823	0.0005	10	-6.4999785535
	11	1.558	1.559	1.5585	0.0065497297	-0.0037457608	0.0014000823	0
	g) f(x)= x^2+ln(x), com Ɛ= 10^-6 (0,000001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	0.1	1	0.55	-2.292585093	1	-0.2953370008	0.55	0.1	-2.292585093
	2	0.55	1	0.775	-0.2953370008	1	0.3457327504	0.255	1	1
	3	0.55	0.775	0.6625	-0.2953370008	0.3457327504	0.0271715289	0.093	2	4.6931471806
	4	0.55	0.662	0.606	-0.2953370008	0.025754277	-0.1336392929	0.056	3	10.0986122887
	5	0.606	0.662	0.634	-0.1336392929	0.025754277	-0.0537503245	0.028	4	17.3862943611
	6	0.634	0.662	0.648	-0.0537503245	0.025754277	-0.0139605826	0.013	5	26.6094379124
	7	0.648	0.662	0.655	-0.0139605826	0.025754277	0.0059049567	0.007	6	37.7917594692
	8	0.648	0.655	0.6515	-0.0139605826	0.0059049567	-0.0040256324	0.004	7	50.9459101491
	9	0.615	0.655	0.635	-0.1079080112	0.0059049567	-0.0509052801	0.016	8	66.0794415417
	10	0.635	0.655	0.645	-0.0509052801	0.0059049567	-0.0224799622	0.01	9	83.1972245773
	11	0.645	0.655	0.65	-0.0224799622	0.0059049567	-0.0082829161	0.005	10	102.302585093
	12	0.65	0.655	0.6525	-0.0082829161	0.0059049567	-0.0011878898	0.002
	13	0.652	0.655	0.6535	-0.0026067171	0.0059049567	0.0016495041	0.001
	14	0.652	0.653	0.6525	-0.0026067171	0.0002308503	-0.0011878898	0.001
	15	0.652	0.653	0.6525	-0.0026067171	0.0002308503	-0.0011878898	0
	h) f(x)= x^2-10x+23, Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	3	4	3.5	2	-1	0.25	3.5	-4	79
	2	3.5	4	3.75	0.25	-1	-0.4375	0.25	-3	62
	3	3.5	3.75	3.625	0.25	-0.4375	-0.109375	0.13	-2	47
	4	3.5	3.62	3.56	0.25	-0.0956	0.0736	0.06	-1	34
	5	3.56	3.62	3.59	0.0736	-0.0956	-0.0119	0.03	0	23
	6	3.56	3.59	3.575	0.0736	-0.0119	0.030625	0.02	1	14
	7	3.57	3.59	3.58	0.0449	-0.0119	0.0164	0.01	2	7
	8	3.58	3.59	3.585	0.0164	-0.0119	0.002225	0.005	3	2
	9	3.58	3.59	3.585	0.0164	-0.0119	0.002225	0	4	-1
	5	-2
	6	-1
	i) f(x)=2x-cos(x), com Ɛ= 10^-4 (0,0001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	0	1	0.5	-1	1.4596976941	0.1224174381	0.5	-3	-5.0100075034
	2	0	0.5	0.25	-1	0.1224174381	-0.4689124217	0.25	-2	-3.5838531635
	3	0.25	0.5	0.375	-0.4689124217	0.1224174381	-0.1805076219	0.125	-1	-2.5403023059
	4	0.37	0.5	0.435	-0.1923273456	0.1224174381	-0.0368700423	0.06	0	-1
	5	0.435	0.5	0.4675	-0.0368700423	0.1224174381	0.0423022834	0.0325	1	1.4596976941
	6	0.435	0.467	0.451	-0.0368700423	0.041077067	0.0019883133	0.0165	2	4.4161468365
	7	0.435	0.451	0.443	-0.0368700423	0.0019883133	-0.0174697754	0.008	3	6.9899924966
	8	0.443	0.451	0.447	-0.0174697754	0.0019883133	-0.007747945	0.004	4	8.6536436209
	9	0.447	0.451	0.449	-0.007747945
0.0019883133	-0.0028816176	0.002	5	9.7163378145
	10	0.449	0.451	0.45	-0.0028816176	0.0019883133	-0.0004471024	0.001	6	11.0398297133
	11	0.45	0.451	0.4505	-0.0004471024	0.0019883133	0.000770493	0.0005	7	13.2460977457
	11	0.4505	0.4505	0.4505	0.000770493	0.000770493	0.000770493	0
	j) f(x)= 8e^-0,5x*cox(3x), com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|	x	f(x)
	1	1	2	1.5	-4.8036864166	2.8258152679	-0.7965830809	1.5	-5	-74.0391472834
	2	1.5	2	1.75	-0.7965830809	2.8258152679	1.7077518903	0.25	-4	49.882273923
	3	1.5	1.75	1.625	-0.7965830809	1.7077518903	0.5747249391	0.125	-3	-32.6672202907
	4	1.5	1.625	1.5625	-0.7965830809	0.5747249391	-0.0911506331	0.0625	-2	20.8801075394
	5	1.562	1.625	1.5935	-0.096666991	0.5747249391	0.2454411619	0.031	-1	-13.0577734958
	6	1.562	1.593	1.5775	-0.096666991	0.2401039492	0.0731046544	0.016	0	8
	7	1.562	1.577	1.5695	-0.096666991	0.0676696427	-0.0141942369	0.008	1	-4.8036864166
	8	1.569	1.577	1.573	-0.0196739003	0.0676696427	0.024086997	0.0035	2	2.8258152679
	9	1.569	1.573	1.571	-0.0196739003	0.024086997	0.00222847	0.002	3	-1.62640513
	10	1.569	1.571	1.57	-0.0196739003	0.00222847	-0.0087172799	0.001	4	0.9136257161
	11	1.57	1.571	1.5705	-0.0087172799	0.00222847	-0.0032430405	0.0005	5	-0.4988718503
	12	1.57	1.571	1.5705	-0.0087172799	0.00222847	-0.0032430405	0
Posição Falsa
	a) f(x)= 1-xln(x), com Ɛ=10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	1	2	1.6666666667	1	-0.3862943611	0.1486239604	1.67
	2	1.67	2	1.89	0.1435845439	-0.3862943611	-0.2031302069	0.2233333333
	3	1.67	1.89	1.8166666667	0.1435845439	-0.2031302069	-0.0845560313	0.0733333333
	4	1.67	1.82	1.77	0.1435845439	-0.089882432	-0.0106337975	0.0466666667
	4	1.67	1.77	1.7366666667	0.1435845439	-0.0106337975	0.0414163251	0.0333333333
	4	1.74	1.77	1.76	0.036239903	-0.0106337975	0.0050476961	0.0233333333
	4	1.76	1.77	1.7666666667	0.0050476961	-0.0106337975	-0.0054003397	0.0066666667
	4	1.76	1.77	1.7666666667	0.0050476961	-0.0106337975	-0.0054003397	0
	b) f(x)= 2^x-3x, com Ɛ=10^-2 (0,01)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	0	1	0.6666666667	1	-1	-0.412598948	0.67
	2	0	0.67	0.4466666667	1	-0.4189270325	0.022887677	0.22
	3	0.45	0.67	0.5966666667	0.0160402568	-0.4189270325	-0.2777814398	0.15
	4	0.45	0.6	0.55	0.0160402568	-0.2842834335	-0.1859143041	0.05
	5	0.45	0.55	0.5166666667	0.0160402568	-0.1859143041	-0.1193540676	0.03
	6	0.45	0.52	0.4966666667	0.0160402568	-0.126044752	-0.0790501929	0.02
	7	0.45	0.5	0.4833333333	0.0160402568	-0.0857864376	-0.0520300658	0.02
	8	0.45	0.48	0.47	0.0160402568	-0.0452563336	-0.0248905319	0.01
	8	0.45	0.47	0.4633333333	0.0160402568	-0.0248905319	-0.011276331	0.01
	8	0.45	0.46	0.4566666667	0.0160402568	-0.0044581819	0.0023673104	0
	c) f(x)= x^3+x-1000, com Ɛ=10^-5 (0,00001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	9	10	9.6666666667	-262	10	-87.037037037	9.67
	2	9.67	10	9.89	-86.098937	10	-22.748331	0.22
	3	9.89	10	9.9633333333	-22.748331	10	-0.9963826296	0.07
	4	9.96	10	9.9866666667	-1.992064	10	5.9919976296	0.03
	4	9.96	9.993	9.982	-1.992064	7.894469657	4.591714168	0.01
	4	9.96	9.98	9.9733333333	-1.992064	3.991992	1.9946477037	0.01
	4	9.96	9.97	9.9666666667	-1.992064	0.996973	-0.000037037	0
	d) f(x)= x^3-2x^2-3x+10, com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	-3	-2	-2.3333333333	-26	0	-6.5925925926
	2	-2.3	-2	-2.1	-5.847	0	-1.781
	3	-2.1	-2	-2.0333333333	-1.781	0	-0.5755925926
	4	-2	-2	-2	0	0	0
	4	0	10	10	10
	e) f(x)= e^x-x-2, com Ɛ= 10^-4 (0,0001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	-2	-1	-1.3333333333	0.1353633504	-0.6320824135	-0.4030330849	1.3
	2	-2	-1.3	-1.5333333333	0.1353633504	-0.4274314701	-0.2508172697	0.2
	3	-2	-1.5	-1.6666666667	0.1353633504	-0.2768351345	-0.1444250886	0.2
	4	-2	-1.7	-1.8	0.1353633504	-0.1172842727	-0.0346702589	0.1
	5	-2	-1.8	-1.8666666667	0.1353633504	-0.0346702589	0.0213348634	0.1
	6	-1.9	-1.8	-1.8333333333	0.0495980872	-0.0346702589	-0.0067565265	0.1
	7	-1.9	-1.8	-1.8333333333	0.0495980872	-0.0346702589	-0.0067565265	0
	f) f(x)= 70e^-1,5x+2,5e^-0,07x-9, com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	1	2	1.6666666667	8.9525420514	-3.3403938598	-1.0278291529	1.67
	2	1	1.67	1.4466666667	8.9525420514	-1.057010652	1.2534854046	0.22
	3	1.45	1.67	1.5966666667	1.2130910885	-1.057010652	-0.3806693161	0.15
	4	1.45	1.6	1.55	1.2130910885	-0.4130262615	0.0894638102	0.05
	5	1.55	1.6	1.5833333333	0.0894638102	-0.4130262615	-0.2496367098	0.03
	6	1.55	1.58	1.57	0.0894638102	-0.2164733231	-0.1159975608	0.01
	7	1.55	1.57	1.5633333333	0.0894638102	-0.1159975608	-0.0481841326	0.01
	8	1.55	1.56	1.5566666667	0.0894638102	-0.0140260454	0.0203007435	0
	g) f(x)= x^2+ln(x), com Ɛ= 10^-6 (0,000001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	0.1	1	0.7	-2.292585093	1	0.1333250561	0.7
	2	0.1	0.7	0.5	-2.292585093	0.1333250561	-0.4431471806	0.2
	3	0.5	0.7	0.6333333333	-0.4431471806	0.1333250561	-0.0556472914	0.13
	4	0.63	0.7	0.6766666667	-0.0651354596	0.1333250561	0.0673012822	0.05
	5	0.63	0.68	0.6633333333	-0.0651354596	0.0767375192	0.0295334612	0.02
	6	0.63	0.66	0.65	-0.0651354596	0.020084556	-0.0082829161	0.01
	7	0.65	0.66	0.6566666667	-0.0082829161	0.020084556	0.0106323652	0.01
	8	0.65	0.66	0.6566666667	-0.0082829161	0.020084556	0.0106323652	0
	h) f(x)= x^2-10x+23, Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	3	4	3.6666666667	2	-1	-0.2222222222	3.67
	2	3	3.67	3.4466666667	2	-0.2311	0.4128444444	0.22
	3	3.45	3.67	3.5966666667	0.4025	-0.2311	-0.0306555556	0.15
	4	3.45	3.6	3.55	0.4025	-0.04	0.1025	0.0466666667
	4	3.55	3.6	3.5833333333	0.1025	-0.04	0.0069444444	0.0333333333
	4	3.58	3.6	3.5933333333	0.0164	-0.04	-0.0212888889	0.01
	4	3.58	3.59	3.5866666667	0.0164	-0.0119	-0.0024888889	0.0066666667
	4	3.58	3.59	3.5866666667	0.0164	-0.0119	-0.0024888889	0
	i) f(x)=2-cos(x), com Ɛ= 10^-4 (0,0001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	0
	2	0	0
	3	0	0
	4	0	0
	4	0	0
	j) f(x)= 8e^-0,5x*cox(3x), com Ɛ= 10^-3 (0,001)
	k	a	b	x	f(a)	f(b)	f(x)	| xk+1 – xk|
	1	1	2	1.6666666667
	2	0
	3	0
	4	0
	4	0
Ponto Fixo
	a) f(x)= 1-ln(x), com Ɛ=10^-3 (0,001)
	K	xk	Q(x)	| xk+1 – xk|
	1	1.800	1.743	0.057
	2	1.743	1.775	0.032
	3	1.775	1.757	0.018
	3	1.757	1.767	0.010
	1.767	1.761	0.006
	1.761	1.764	0.003
	1.764	1.763	0.002
	1.763	1.764	0.001
	1.764	1.763	0.001
	1.763	1.763	0.000
	c) f(x)= x^3+x-1000, com Ɛ=10^-5 (0,00001)
	K	xk	Q(x)	| xk+1 – xk|
	1	9.500	9.968	0.468
	2	9.968	9.967	0.002
	3	9.967	9.967	0.000
Newton - Raphson
	c) f(x)= x^3+x-1000, com Ɛ=10^-5 (0,00001)
	K	xk	xk+1 	| xk+1 – xk|
	1	9.50000	9.98988	0.48988
	2	9.98988	9.96672	0.02316
	3	9.96672	9.96667	0.00005
	4	9.96667	9.96667	0.00000