Exercício de Cálculo Diferencial e Integral - III - Exercício de Fixação 2-2

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Exercício de Cálculo Diferencial e Integral - III - 
Exercício de Fixação 2 - Tentativa 2 de 3 
Questão 1 de 10 
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A - image.png 1.64 KB 
B - image.png 1.64 KB 
C - image.png 1.64 KB Resposta correta 
D - image.png 1.54 KB 
E - image.png 1.62 KB 
 
Questão 2 de 10 
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B - image.png 434 Bytes Resposta correta 
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E - image.png 432 Bytes 
 
Questão 3 de 10 
Seja uma função de duas variáveis reais definida pela expressão: 
 
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Sabemos que as curvas de nível do tipo f(x,y)=c representam lugares geométricos específicos no 
plano cartesiano. Com base nos conteúdos discutidos ao longo da disciplina de Cálculo Diferencial e 
Integral III e do livro-base (MELO, C. F. Cálculo Diferencial e Integral III, Curitiba: FAEL, 2015), marque a 
alternativa que apresenta a interpretação correta das curvas de nível dadas por: 
 
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A - Cada curva de nível é um círculo com centro na origem. Resposta correta 
B - Cada curva de nível é uma hipérbole com centro na origem. 
C - Cada curva de nível é um círculo centrado no ponto (x,y). 
D - Cada curva de nível é uma elipse centrada no ponto (x,y). 
E - Cada curva de nível se degenera em um único ponto. 
 
Questão 4 de 10 
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A - I e II, somente. 
B - I e III, somente. 
C - II e III, somente. 
D - III, somente. 
E - I, II e III. Resposta correta 
 
Questão 5 de 10 
Um triângulo retângulo tem medidas de seus catetos iguais a 3 cm e 8 cm. Utilizando 
diferenciais, determine uma aproximação para a variação da área desse triângulo, se suas 
medidas variam para 2,7 cm e 8,9 cm. 
 
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B - image.png 462 Bytes 
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C - image.png 471 Bytes Resposta correta 
D - image.png 435 Bytes 
E - image.png 438 Bytes 
 
Questão 6 de 10 
Suponha a existência de uma função f definida para duas variáveis, x e y, dada por: 
 
 
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Sabemos que podemos calcular o limite de uma função desse tipo quando analisamos o 
comportamento de f(x,y) quando (x,y) se aproxima de um determinado par de pontos. Com base nos 
conteúdos discutidos ao longo da disciplina de Cálculo Diferencial e Integral III e do livro-base (MELO, 
C. F. Cálculo Diferencial e Integral III, Curitiba: FAEL, 2015), marque a alternativa que apresenta o 
limite da função dada quando (x,y) tende ao ponto (3,2). 
A - 7/3 
B - 3/7 
C - 13/17 
D - 17/13 Resposta correta 
E - 1/3 
 
Questão 7 de 10 
Suponha a existência da função f definida para duas variáveis reais, digamos x e y, definida 
por: 
 
 
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Sabemos que o cálculo das derivadas parciais é realizada para uma determinada variável, mantendo 
constantetodas as demais, a título de resolução. Com base nos conteúdos discutidos ao longo da 
disciplina de Cálculo Diferencial e Integral III e do livro-base (MELO, C. F. Cálculo Diferencial e Integral 
III, Curitiba: FAEL, 2015), marque a alternativa que apresenta o valor correto da derivada parcial de 
f(x,y) em relação a x. 
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E - image.png 838 Bytes 
 
Questão 8 de 10 
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A - -0,1 
B - 0,1 
C - -0,2 
D - 0,2 
E - 0,5 Resposta correta 
 
Questão 9 de 10 
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B - image.png 1.5 KB 
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C - image.png 1.45 KB Resposta 
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E - image.png 1.55 KB 
 
Questão 10 de 10 
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A - - 0,1 e 0,0998 
B - 0,1 e - 0,0998 
C - - 0,2 e 0,2445 
D - -0,5 e 0,4995 
E - 0,5 e - 0,4995 Resposta correta 
 
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