<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Aplica\303\247\303\243o</Text-field>

O Teorema do Valor Intermedi\303\241rio tem muitas aplica\303\247\303\265es. Uma aplica\303\247\303\243o cl\303\241ssica de TVI \303\251 o M\303\251todo da Bisse\303\247\303\243o ( Bisection Method). O M\303\251todo da Bisse\303\247\303\243o ( Bisection Method) \303\251 um algor\303\255tmo para encontrar uma aproxima\303\247\303\243o para um zero ( zero ) de uma fun\303\247\303\243o cont\303\255nua.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 8.1 - M\303\251todo da Bisse\303\247\303\243o </Text-field>

Considere a fun\303\247\303\243o

f := x -> (x^5 - 4*x^2 + 2)/(x-1): 'f'(x) = f(x);

Figura 8.1, um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== sugere que existem pelo menos tr\303\252s solu\303\247\303\265es reais paraLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= 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 .

plot( f(x), x=-2..3, y=-10..10, discont=true );

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

Figura 8.1

O gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1JJm1mcmFjR0YkNigtRiM2JkYrLUYjNilGKy1GIzYmRistSSVtc3VwR0YkNiVGXG8tSSNtbkdGJDYkUSI1RidGQC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0ZALUY9Ni1RKCZtaW51cztGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGYXEtRiM2Jy1GZ3A2JFEiNEYnRkAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRmRwNiVGXG8tRmdwNiRRIjJGJ0ZARmpwRitGQC1GPTYtUSIrRidGQEZCRkVGR0ZJRktGTUZPRmBxRmJxRl1yRkBGK0ZALUYjNiZGKy1GIzYmRlxvRl1xLUZncDYkUSIxRidGQEZARitGQC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3MvJSliZXZlbGxlZEdGREYrRkBGK0ZA sugere que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2MkYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRiw2JVEkdGVtRicvRjdGREZARmRvLUYsNiVRJXBlbG9GJ0Zqb0ZARmRvLUYsNiVRJm1lbm9zRidGam9GQEZkb0Zkby1GLDYlUSt0ciZlY2lyYztzRidGam9GQEZkby1GLDYlUSZ6ZXJvc0YnRmpvRkBGZG8tRiw2JVEmcmVhaXNGJ0Zqb0ZARkBGK0ZA

Aparece como se uma das solu\303\247\303\265es para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1JI21uR0YkNiRRIjBGJ0ZARkBGK0ZA estivesse no intervalo fechado 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. O TVI confirma isto, como a fun\303\247\303\243o f \303\251 cont\303\255nua em 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 e 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 > 0 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUkjbW5HRiQ2JFEiMEYnRkBGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZpby1GIzYlLUY9Ni1RKiZ1bWludXMwO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRl1vNiRRIjJGJ0ZARkBGK0ZARitGQA== < 0.

O M\303\251todo da Bisse\303\247\303\243o leva isto mais adiante.

Passo 1: O ponto m\303\251dio ( midpoint) de 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 \303\251 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 ; porque 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 < 0 o TVI nos diz que a solu\303\247\303\243o ser\303\241 encontrada em 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 .

Passo 2: O ponto m\303\251dio de 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 \303\251 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 ; porque 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 > 0 o TVI nos diz que a solu\303\247\303\243o ser\303\241 encontrada em 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 .

Pode-se continuar este processo at\303\251 o intervalo ser suficientemente pequeno. Para implementar isto no Maple, denominar como max_len o comprimento do intervalo quando a itera\303\247\303\243o deve parar. O seguinte c\303\263digo Maple implementa o M\303\251todo da bisse\303\247\303\243o.

C\303\263digo para o M\303\251todo da Bisse\303\247\303\243o

bisect := proc( f::procedure, II::range, max_len::positive ) local a, b, c; a := op(1,II); b := op(2,II); if signum(f(a))=signum(f(b)) or not iscont(f(x),x=II) then error "the IVT does not apply on the interval", II end if; while abs(b-a)>max_len do c := (a+b)/2; if f(c)=0 then break elif signum(f(a))=signum(f(c)) then a := c else b := c end if; end do: return( [a..b] ) end proc:

Definir uma toler\303\242ncia selecionando um comprimento maximum para o intervalo contendo a raiz( root).

max_len := 10^(-4):

Quando o M\303\251todo da Bisse\303\247\303\243o for reiniciado em 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 com uma toler\303\242ncia de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSMxMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmRistRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUi1GMzYkUSI0RidGNkY2RitGNi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y2 = 0.0001, o intervalo contendo a raiz ser\303\241 encontrado

bisect( f, -1...0., 10^(-4) );

A conclus\303\243o de que esta raiz ocorre em [-0.680786, -0.680725] \303\251 consistente com o resultado do comando Maple's fsolve , a saber,

fsolve( f(x)=0, x );

As outras raizes desta fun\303\247\303\243o podem ser aproximadas da mesma forma. Note que TVI n\303\243o pode ser aplicado em 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 , 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 , ou qualquer intervalo contendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=, porque a fun\303\247\303\243o tem uma ass\303\255ntota ( asymptote) vertical em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= (portanto n\303\243o pode ser cont\303\255nua l\303\241). Isto n\303\243o \303\251 dif\303\255cil porque sabemos 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 e 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 . Para a menor raiz positiva(positive), podemos aplicar o M\303\251todo da Bisse\303\247\303\243o em [0, 0.99].

Primeiro, precisamos saber que os valores da fun\303\247\303\243o muda o sinal (sign) dentro deste intervalo.

f(0), f(0.99);

Ent\303\243o, o resultado do M\303\251todo da Bisse\303\247\303\243o \303\251

bisect( f, 0..0.99, 10^(-4) );

e o intervalo \303\251 comparado ao valor do Maple para a raiz via

fsolve( f(x)=0, x, x=0..0.99 );

De novo o resultado \303\251 consistente com a aproxima\303\247\303\243o do Maple para esta solu\303\247\303\243o:

A segunda raiz positiva pode ser encontrada aplicando o M\303\251todo da Bisse\303\247\303\243o em [1.01, 2]. Primeiro, precisa haver uma mudan\303\247a de sinal dentro do intervalo, como mostrado em

f(1.01), f(2);

Ent\303\243o, o resultado do M\303\251todo da Bisse\303\247\303\243o \303\251

bisect( f, 1.01..2, 10^(-4) );

e este intervalo se compara favoravelmente com a aproxima\303\247\303\243o do Maple para a raiz encontrada via

fsolve( f(x)=0, x , x=1.01..2 );

Outras aplica\303\247\303\265es de TVI s\303\243o menos \303\263bvias.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 8.2 - Termperaturas <Hyperlink linktarget="Dictionary:Definition,periodicfunction" hyperlink="true">Peri\303\263dicas(Periodic)</Hyperlink></Text-field>

Suponha que a temperatura \303\251 55 graus \303\240 meia noite, aumenta at\303\251 a altura de 85 graus, ent\303\243o retorna para 55 graus \303\240 meia noite do dia seguinte. Suponha que a temperatura durante o dia \303\251 uma fun\303\247\303\243o cont\303\255nua do tempo di\303\241rio.

Use o TVI para mostrar que existe pelo menos um hor\303\241rio da manh\303\243 em que a temperatura \303\251 a mesma que a temperatura exatamente 12 horas depois.

Se 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 denota a temperatura (em graus) no tempo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSUmbGU7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEjMjRGJ0Y1RjVGK0Y1. Definir a fun\303\247\303\243o f por 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSUmbGU7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEjMTJGJ0Y1RjVGK0Y1. Ent\303\243o

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 = 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 = 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 .

Caso 1: Se 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 est\303\243o a 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 = 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 e n\303\263s temos duas vezes, com 12 horas de diferen\303\247a, quando as temperaturas s\303\243o iguais.

Caso 2: Se 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 , ent\303\243o 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 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiQtSSNtbkdGJDYkUSMxMkYnRj5GPi1GOzYtUSIpRidGPkZZRkNGWkZHRklGS0ZNRmVuL0ZTUSwwLjExMTExMTFlbUYnRj5GK0Y+RitGPg== t\303\252m sinais diferentes. Como T \303\251 cont\303\255nua durante o dia, f deve ser cont\303\255nua em [0, 12]. O TVM pode ser ampliado para concluir que existe um tempo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjdCpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn em (0, 12) quando 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 ; isto \303\251, 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 .

Desde que exatamente um dos dois casos deve ser verdadeiro, a prova ( proof) est\303\241 completa. (Note que n\303\243o requer a informa\303\247\303\243o sobre a altura da temperatura).