Julgue a afirmativa:

Item 4 - Seja r a reta tangente ao gráfico de !$ y = 2x^2 - 3x + 5 !$, no ponto (1,4). A equação da reta perpendicular a r e que passa por (-1,2) é y = −x +1.

É correta a afirmativa:

Item 0 - Considere dois estimadores não tendenciosos, !$ \hat{ \theta}_1 !$ e !$ \hat{ \theta}_2 !$, de um parâmetro !$ \theta. \hat{ \theta}_1 !$ é eficiente relativamente a !$ \hat{ \theta}_2 !$ se var!$ ( \hat{ \theta}_1) < var( \hat{ \theta}_2) !$;

Julgue a afirmativa:

Item 3 - Se S é um subconjunto de IR³ formado por vetores linearmente dependentes, então podemos afirmar que S tem 4 elementos ou mais;

Sobre o processo de crescimento e diversificação da indústria manufatureira na primeira década após a Segunda Guerra Mundial, é correto afirmar que:

Item 2 - A política econômica do Governo Eurico Dutra iniciou reduzindo a proteção da indústria local, mas posteriormente adotou uma política cambial que favoreceu a substituição de importações;

Considere as funções definidas por

!$ f(x) = { \Large {2x^2 \over x^2 -1}} !$ e !$ g(x)= x^3 = 9x^2 + 24 x - 20 !$ .Julgue a afirmativa:

Item 0- g atinge máximo relativo em x = 2 e mínimo relativo em x = 4;.

When Edwin Hubble, the astronomer after whom the space telescope is named, looked at the skies in the 1920s using what was then the world’s largest telescope, he found that there were galaxies outside the Milky Way, an observation that profoundly shocked his contemporaries. Max Planck founded quantum theory, and thus wrecked the Newtonian universe. And William Herschel discovered Uranus, the first planet unknown to the astrologers of old. If the new and refurbished instruments named after these scientific mould-breakers do as much in the next few years as their eponyms did, it will, indeed, be an exciting time for astronomy and physics.

According to the text

Item 4 - Uranus was first seen by Edwin Hubble.

A propósito da desaceleração da economia brasileira na primeira metade dos anos 1960, é correto afirmar que:

Item 0 - A resistência do Congresso Nacional foi fator importante para inviabilizar a realização das reformas estruturais propostas pelo Governo João Goulart para combater a crise;

Uma empresa produzindo bolas de futebol possui função de produção !$ Q = 2 \sqrt{KL} !$. Suponha que no curto prazo a quantidade de capital é fixa em !$ \bar{K} = 100 !$, e seja L a quantidade de trabalho. Responda V ou F à seguinte alternativa:

Item 3 - Esta função de produção possui produto marginal decrescente para o trabalho;

Com relação ao chamado “Milagre Brasileiro” (1968-1973), pode-se afirmar que a política econômica adotada no período teve a seguinte característica:

Item 1 - As isenções fiscais e os juros subsidiados à agricultura visaram ao aumento da oferta de alimentos e ao crescimento das exportações de produtos primários;

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)

According to the text

Item 1 - astronauts have never been transported by the space shuttle;