Sejam !$ f : IR_+^* \rightarrow IR\ !$ e !$ g: [ - \sqrt{5}, \sqrt{5} ] \rightarrow IR\ !$ funções tais que f(x) = ln x e !$ g(x) = x \sqrt{5 - x^2} !$. Julgue a afirmativa:

Item 1 - !$ \int { \Large { x \over x^2 + 7}} dx = { \Large { f (x^2 + 7) \over 2}} + c !$, em que c é uma constante arbitrária;

Considerando-se os efeitos das aberturas comercial e financeira da década de 1990 sobre o crescimento econômico, a estrutura produtiva e o balanço de pagamentos é correto afirmar que:

Item 3 - Entre 1995 e 1998, os déficits comerciais da indústria manufatureira foram inteiramente financiados pelo superávit agrícola;

Considere uma economia descrita pelas seguintes equações:

• Produção de bens: !$ Y = K^a (EL_Y)^{ 1- a},\,\,\,\,\,\,\,0 !$

• Produção de “conhecimento”: !$ \dot{E} = \delta L_E E^{\phi},\,\,\,\,\,\,0 \ge \ge 1,\,\,\,0 < \delta < 1 !$

• Acumulação de capital: !$ \dot{K} = sY - dK,\,\,\,\,\,0< s<1,\,\,0< d < 1 !$

• Restrição de trabalho:!$ L = L_Y + L_E,\,\,\,\,\,\,L>0 !$

Em que Y é o produto, K é o estoque de capital, E é o nível de “conhecimento” na economia e L_Y, L_E e L representam, respectivamente, os trabalhadores empregados na produção de bens, na produção de conhecimento e o total de trabalhadores. O número de trabalhadores na produção de conhecimento é uma fração constante, u, da força de trabalho:!$ L_E = uL, 0 < u < 1 !$. A taxa de crescimento da força de trabalho L é constante e igual a n, ou seja, !$ \dot{L} /L = n !$. Com base nessas informações, julgue a seguinte afirmativa:

Item 0- Se !$ \phi = 0 !$ e !$ n = 0 !$, a economia apresenta uma trajetória de crescimento equilibrado, na qual o produto (Y) cresce a uma taxa constante e positiva;

Julgue a afirmativa:

Item 1- Se !$ a \ge 0 !$ e !$ b \ge 0 !$, então !$ \underset {n \rightarrow \infty} {lim} \sqrt[n]{ a^n + b^n} = max \left \{a,b \right \} !$;

Seja !$ \Phi (x,y) = xy !$ a função real definida no quadrante !$ A = \left \{ (x,y) | x ge 0\,e\,y \ge 0 \right \} !$

Julgue o item abaixo:

Item 0 -A declividade da reta tangente à curva !$ \Phi (x,y) =1 !$ no ponto (1,1) é igual a -2;

Dentre as transformações ocorridas na economia brasileira a partir dos anos 1990 pode-se arrolar:

Item 2 - redução da informalidade, com o crescimento dos empregos com carteira assinada;

Text 2

Excerpts from:

Peek-a-boo

Astronomers get some new toys to play
with

FEW scientists believe that the space shuttle has helped their profession. Mostly, it has been used to convey astronauts to a space station that has produced little worthwhile research and to launch satellites that might have been put into orbit more cheaply by old-fashioned, throwaway rockets. But it has done one thing to assist astronomers. It has allowed what is probably their most famous instrument to be repaired and upgraded. That instrument is the Hubble space telescope, which took the picture of the Carina nebula shown above, and has snapped more than half a million other images over the years. Now, as the shuttle programme draws to its close (the final launch will take place next year), Hubble is to be given its last makeover by the crew of Atlantis. On top of that, if the week has gone well, two other satellites intended to probe the universe’s earliest days will have been launched.

The mission to Hubble, which began on May 11th and is planned to last 11 days, will install a wide-field camera that will let the telescope see galaxies previously beyond its reach. Using this, the eager coteries of astronomers who have access to the instrument will be able to observe young, hot stars that glow mainly in the ultraviolet part of the spectrum. They will also be able to see the first stars and galaxies that formed in the universe, which are now so old and distant that their light has been relegated to the infra-red part of the spectrum by the “red shift” caused by the universe’s expansion. These wonders can be observed only from space, because ozone and water in the Earth’s atmosphere absorb light at those wavelengths.

(...)

(From The Economist print edition, May 14^th 2009)

We can infer from the text that

Item 2 - the space shuttle has been mainly used to take scientists to a space station;

Considere o jogo conhecido como “caça ao cervo”, abaixo:

Em que !$ 0 \le x < 1 !$ é constante. Com base nesse jogo, avalie a afirmação abaixo:

Item 0- Trata-se de um jogo de informação imperfeita;

Text 1

Excerpts from:

Fiat's ambitions

The Italian solution

Fiat’s chief executive, Sergio Marchionne,
has gone merger mad

HIS company is among the smallest of the global volume carmakers. But right now Sergio Marchionne is without question the most talked-about car executive in the world. The chief executive of Fiat Group has been alone in seeing an extraordinary opportunity in the meltdown in Detroit. By seeking to take over the running of both Chrysler and Opel, the European arm of General Motors (GM), Mr Marchionne is attempting not only to transform Fiat into a car group almost of the scale of mighty Toyota and Volkswagen (VW), but also to change the face of a perennially troubled industry.

Last December Mr Marchionne said of his stricken industry: “What we are seeing is unprecedented. I have never seen the failure of so many systems at once.” Fiat was in a fight for survival. “We’re just going to slam the brakes on, use as many temporary lay-offs as needed, cut everything back to essentials.” He added an apocalyptic forecast. “By the time we finish with this in the next 24 months, as far as mass producers are concerned, we’re going to end up with one American house [Ford or GM, you presume]; one German of size [VW Group]; one French-Japanese, maybe with an extension in the US [the Renault-Nissan alliance]; one in Japan [Toyota], one in China [several possible candidates] and one potential European player [either Fiat or PSA Peugeot Citroën].”

The details of this vision may be wrong. Despite its present travails and imminent bankruptcy, few believe that GM will vanish and leave Ford as the sole American-owned champion. France’s PSA Peugeot Citroën, though unwieldy, is not about to disappear either. The strength of Hyundai- Kia in emerging markets and North America should ensure that the South Korean producer makes the cut. And in Japan, however great the cull of smaller outfits such as Mitsubishi and Suzuki, Honda and perhaps Mazda will still be around to challenge the dominance of Toyota in its home market. So will Renault’s partner, Nissan.

(…)

Having presided over a near-miraculous turnaround at Fiat since being appointed in 2004, Mr Marchionne saw in Chrysler an opportunity to apply the same lessons. At Fiat he saw a sluggish organisation that lacked leadership and had become accustomed to management by committee. But he also saw, buried within the company, a new generation of leaders.

“The single most important thing was to dismantle the organisational structure,” he recalls. “We tore it apart in 60 days, removing a large number of leaders who had been there a long time and who represented an operating style that lay outside any proper understanding of market dynamics.” In their place he promoted a group of younger executives, many with a background in consumer marketing, who understood and could provide what he wanted: accountability, openness, rapid communication and impatience with hierarchy and internal politics.

Some doubt that Fiat’s lean management has the resources to spread itself across Chrysler, let alone Opel too. Mr Marchionne understands the concern, but rejects it. He believes he already knows who the new leaders at Chrysler will be. He is confident that the same will apply to Opel, should that too fall into his lap.

(…)

(From The Economist print edition, May 7th 2009)

The text implies that

Item 4 - Mr. Marchionne took over two months to dismantle the old structure.

Responda se verdadeiro ou falso:

Item 4 - Se um estimador convergir em média quadrática para o parâmetro, ele será consistente (convergirá em probabilidade para o parâmetro).