Foram encontradas 40 questões.
O professor de Cálculo Diferencial e Integral do curso de engenharia estava ensinando os limites conhecidos como fundamentais para as demandas de Séries em Cálculo. Em sua explicação, propôs a demonstração do \( \lim_{x \rightarrow 0^\circ} \dfrac{\text{sen } x}{x} \). Sendo assim, após a demonstração, chegou ao resultado:
Provas
Considere as curvas \( y = x^2 - 2x + 2 \), \( y = x \). A região \( R \) limitada por essas curvas é rotacionada em torno da reta \( x = 3 \). O volume do sólido gerado por essa rotação é:
Provas
Considere \( T : \mathbb{R}^4 \rightarrow \mathbb{R}^4 \) definida por \( T(v) = Av \), em que
\( A = \begin{pmatrix} 1 & 2 & -1 & 0 \\ 2 & 4 & -2 & 0 \\ 1 & 1 & 0 & 1 \\ 0 & -1 & 1 & 1 \end{pmatrix} \)
O núcleo de \( T \) é o subespaço de \( \mathbb{R}^4 \) gerado por:
Provas
Considere as afirmativas abaixo:
I) Se \( f(x) \) é uma função crescente de \( \mathbb{R} \rightarrow \mathbb{R} \), então \( f'(x) > 0 \), para todo \( x \in \mathbb{R} \).
II) Sejam \( f \) e \( g \) funções deriváveis em \( \mathbb{R} \), se o \( \lim_{x \rightarrow a} \dfrac{f(x)}{g(x)} \) tem inicialmente indeterminação \( \dfrac{0}{0} \), isso implica \( \lim_{x \rightarrow a} \dfrac{f(x)}{g(x)} = \lim_{x \rightarrow a} \dfrac{f'(x)}{g'(x)} \), onde \( a \in \mathbb{R} \) ou impróprio.
III) O domínio de \( f(x) = \left( 1 + \dfrac{1}{x} \right)^x \) é \( \mathbb{R} - \{-1\} \), no campo dos reais.
IV) A função:
\( f(x,y) = \begin{cases} (x^2+y^2) \text{sen}^3 \left( \dfrac{1}{2x^3+3x^2} \right), & \text{se } (x,y) \neq (0,0) \\ 0, & \text{se } (x,y) = (0,0) \end{cases} \)
é contínua em \( (0,0) \).
Assinale a alternativa correta:
Provas
Calcule o valor da integral \( \int_{2}^{3} \dfrac{\theta^4-2\theta^2+4\theta+1}{\theta^3-\theta^2-\theta+1} d\theta \).
Provas
Considere a região \( R \) do plano \( xy \) delimitada pela equação \( (x^2 + y^2)^3 = 9(x^2 - y^2)^2 \). Sendo assim, encontre a área total dessa região, em unidade de área.
Provas
Considere a sequência (23, 36, 65, 116…). Sendo assim, o valor do décimo termo é:
Provas
Um tanque contém uma substância cuja quantidade \( y(t) \) em \( kg \) varia com o tempo (em horas) de acordo com a equação:
\( \dfrac{dy}{dx} = 2 - ky \), com \( k > 0 \), em que \( k \) é uma constante decaimento. Sendo assim, o que ocorre quando o tempo tende a infinito?
Provas
Read the text below and choose the correct option in question.
Text 4
Why Ship Groundings Matter in Maritime Operations
Ship groundings are more than just embarrassing mishaps; they are high-risk events with far-reaching consequences. According to the International Union of Marine Insurance (IUMI), groundings account for nearly 30% of all hull and machinery claims. The International Maritime Organization (IMO) and port authorities have ramped up pressure on shipping companies to adopt safer navigation protocols, especially in confined and congested waters.
Moreover, groundings often lead to significant environmental consequences. The 2002 grounding of the Prestige oil tanker off the coast of Spain spilled over 60,000 tonnes of oil, affecting over 1,000 km of shoreline. The cost? Billions in cleanup, legal penalties, and reputational damage. In this context, understanding and mitigating grounding risks is a shared responsibility between mariners, shipping companies, regulators, and technology developers.
Which option correctly completes the blank below?
The sentence “The International Maritime Organization (IMO) and port authorities have ramped up pressure on shipping companies […]” means that these bodies on maritime operators.
Provas
Read the text below and choose the correct option in question.
Text 3
Time to reinvent the lifeboat?
Members of the Container Ship Safety Forum (CSSF) have issued a call for a fundamental rethink of the design of lifeboats and lifeboat launching mechanisms on cargo ships. For too long, the focus has been on training and compliance, rather than rethinking the process to eliminate the risk at source.
‘We need to reinvent the lifeboat and its launching equipment onboard cargo vessels. For way too long, we have seen able seafarers being injured when launching lifeboats even though crews have been trained and the lifeboat is modern and fully compliant’, said Aslak Ross, Chairman of the CSSF. ‘Everyone knows we have a problem; seafarers are scared to launch lifeboats; however, no one has offered a plausible path towards a solution to the problem for cargo vessels. A change is needed to provide a safe environment for seafarers and to regain trust in lifesaving equipment’.
In 2017, the UK Chamber of Shipping issued an article ‘Lifeboat drills: We need to save lives, not lose them’ in which they identified 60 fatalities during testing of lifeboats over a 10-year period. ‘Simulation and use of new technology are ways to conduct drills in a safer environment, and we support the intent to reduce the risk of accidents, however, it does not solve the core of the problem: Launching a lifeboat is too dangerous. And even though simulation has its advantages, it should only be used as a supplement to well-conducted onboard abandon ship drills where crews are familiarised with the ship specific equipment’, said Ross. Alternative designs are already available for offshore installations and for passenger evacuation on PAX vessels through Marine Evacuation Systems (MES) and the like, he pointed out. ‘Such systems should also be made available to cargo vessels without delay. It is long overdue to change the current environment and innovate to eliminate the risk of lifeboat accidents. We need approved systems that can be fitted to new buildings – we need to safeguard our seafarers’, Ross concludes.
In the sentence “It is long overdue to change the current environment and innovate to eliminate the risk of lifeboat accidents”, the phrase in bold is closest in meaning to:
Provas
Caderno Container