Prova de Cálculo Diferencial e Integral - III - Avaliação Discursiva - Tentativa 1 de 1

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Prova de Cálculo Diferencial e Integral - III - 
Avaliação Discursiva - Tentativa 1 de 1 
Questão 1 de 10 
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B - image.png 5.14 KB 
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E - image.png 5.3 KB 
Resposta correta 
 
Questão 2 de 10 
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I. A derivada parcial no ponto (0,1) é (0,1) 
II. A derivada parcial no ponto (1,0) é (1,5) 
III. A derivada parcial em relação a x é 15 
 
 
Assinale a alternativa correta: 
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A - Apenas II e III. 
 
B - Apenas I e III. 
 
C - Apenas III. 
 
D - Apenas II. 
 
E - Apenas I. 
 Resposta correta 
 
Questão 3 de 10 
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B - image.png 4.54 KB 
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E - image.png 6.05 KB Resposta correta 
 
Questão 4 de 10 
A soldagem com eletrodo revestido é um processo a arco elétrico produzido entre um 
eletrodo e a peça a ser soldada. Assim, o eletrodo é consumido à medida que vai se 
formando o cordão de solda, cuja proteção contra contaminações do ar atmosférico é feita 
por atmosfera gasosa e escória, proveniente da fusão do seu revestimento. 
 
Supondo que para obter o calor necessário entre duas partes metálicas seja dado por: 
 
image.png 8.5 KBem minutos. 
 
De acordo com o texto, assinale a alternativa que representa quanto tempo é preciso para 
poder iniciar o processo de soldagem? 
A - 6 minutos Resposta correta 
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B - 15 minutos 
C - 10 minutos 
D - 9 minutos 
E - 3 minutos 
 
Questão 5 de 10 
Ao tratar de funções de duas variáveis, as derivadas de 1º ordem devem ser determinadas 
levando em consideração a variável que se está derivando, mantendo a outra constante, 
desde que exista o limite. Já a interpretação geométrica das derivadas parciais de uma 
função com duas variáveis, é semelhante à interpretação das derivadas de uma variável, 
conforme representado na figura abaixo: 
 
 
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A interpretação geométrica das derivadas parciais de primeira ordem de f é: 
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KB Resposta correta 
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Questão 6 de 10 
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Resposta correta 
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E - image.png 5.27 KB 
 
Questão 7 de 10 
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A - As derivadas parciais são descontínuas. 
 
B - A derivada parcial em relação a x no ponto x = 0 é 2. 
 
C - A derivada parcial em relação a x é contínua. 
 Resposta correta 
D - A derivada no ponto (0,0) é igual a (1,1). 
 
E - A derivada parcial em relação a y é descontínua. 
 
Questão 8 de 10 
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A - Basta a terceira condição ser satisfeita para a função ser descontinua. 
 
B - Basta as duas primeiras condições serem satisfeitas para a função ser contínua. 
 
C - Se as duas primeiras condições forem satisfeitas a função será contínua. 
 
D - Se apenas a terceira condição for satisfeita, a função será descontínua. 
 
E - Se uma das condições não for satisfeita a função será descontínua. 
 Resposta correta 
 
Questão 9 de 10 
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A -
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C -
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Questão 10 de 10 
Para se conseguir provar que o limite de uma função de duas ou mais variáveis não existe, mostra-se que o 
limite por dois caminhos distintos são diferentes. Porém, o fato dos dois caminhos escolhidos encontrarem o 
limite da função igual a zero, não implica que o limite desta função seja zero, pois pode-se encontrar um 
terceiro caminho, no qual o limite não seja zero. Para resolver este problema, usa-se o Teorema do 
Confronto. 
 
Considerando as funções g(x,y), f(x,y) e h(x,y), onde f(x,y) está entre as funções g(x,y) e h(x,y), ou seja: 
g ≤ f ≤ h, e o limite das funções tendendo para (x,y) → (a,b). 
 
O teorema do confronto está definido corretamente em: 
A - Se o limite de g(x,y) = L e o limite de h(x,y) = L, então o limite de f(x,y) = L. 
 Resposta correta 
 
B - Se o limite de g(x,y) = L e o limite de f(x,y) = L, então o limite de h(x,y) = L+L. 
 
C - Se o limite de f(x,y) = L e o limite de h(x,y) = L, então o limite de g(x,y) = L. 
 
D - Se o limite de g(x,y) = L e o limite de h(x,y) = L, então o limite de f(x,y) = L+L. 
 
E - Se o limite de g(x,y) = L e o limite de h(x,y) = L, então o limite de f(x,y) = 2L. 
 
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