(06.01 HC) A cоntinuоusly decreаsing functiоn thаt is concаve down on the interval [0, 4] is represented by the table. x 0 1.2 2.7 3.5 4 f(x) 0 −1.44 −7.29 −12.25 −16 Part A: Find the right Riemann sum estimate of using the subintervals given in the table. (10 points) Part B: Find the left Riemann sum estimate of using the subintervals given in the table. (10 points) Part C: Find the trapezoidal estimate of using the subintervals given in the table. (15 points) Part D: Determine whether the right Riemann sum estimate is an overestimate or an underestimate, based on the properties of the function. (5 points)
Je ___________________ un shоrt et un tee-shirt pоur jоuer аu bаsket.
Est-ce que tа fille ________________ lа télé chаque après-midi?
Whаt Mаde Picаssо Picassо? Inevitably, the genius mоves to the metropolis or a university. In 1904, Picasso abandoned Spain for Paris, taking up residence in the heights of Montmartre, then a scruffy suburb where progressive artists could live cheaply and look southward down on the rest of humanity. Van Gogh had lived there, and so had the composer Erik Satie. Penurious painters clumped together in a tenement building called the Bateau-Lavoir because it appeared to be just that—a laundry boat. Picasso’s quarters therein were squalid. But “poverty coupled with genius” attended him, said the poet Max Jacob. And so, too, did other artists and their ideas. But what made Picasso Picasso? In a word: imagination. Pretend for a moment that you are watching Picasso paint. Actually, you are urged to do so in the twelve-minute film The Mystery of Picasso (portions available on YouTube). In the film The Mystery of Picasso, the artist starts from an obscure point to draw a bouquet of flowers, which he turns into a fish, and then a rooster, and finally a clown-like cat. Had the camera not run out of film, Picasso’s imaginings could have run on forever--the ultimate flat-line of creativity. Notice, too, his laserlike stare. Many of his contemporaries commented on his Picasso’s intensely focused eyes. Concentration (maybe obsession) is a constant companion of the creative mind. Picasso could stand upright before a painting for three or four hours at a stretch: “I asked him if it didn’t tire him to stand so long in one spot. He shook his head. ‘No,’ he said. ‘That’s why painters live so long. While I work, I leave my body outside the door, the way Muslims take off their shoes before entering the mosque.” Sometimes Picasso is bewitched and sometimes a somnambulist. Gilot mentions the importance of dreams to Picasso, as if these imaginings might account for the strange forms that appear in his mature works: “I dreamed that my legs and arms grew to an enormous size and then shrank back just as much as in the other direction. And all around me, in my dream, I saw other people going through the same transformations, getting huge or very tiny. I felt terribly anguished every time I dreamed about that.” Invention, fantasy, dreams—the power of the imagination differentiates Pablo Picasso. Picasso’s imagination was endlessly inventive, and his capacity to convert his visions into lines and colors was fast and fluent. But without some mystery, there is no genius. What does the word scruffy mean as it is used in the passage?
The Genius оf Psychic Terrоr: Pаblо Picаsso Picаsso has been called THE genius of the twentieth century. Perhaps more than any single painter, he changed the direction of art, inaugurating the modernist style. He was a pioneer of Cubism, and later of collage art, and then neo-classicism. He was the first to paint most fully his own mind, rather than the object before him. After Picasso, no subject matter was off limits to artistic expression. And still today his Les Demoiselles d’Avignon and Guernica are iconic works known to every art lover. As someone who had often sat at table with Picasso, Gertrude Stein understood that he was a real genius. The Self-Education of a Prodigy Pablo Diego José Francisco de Paula Juan Nepomuceno María de los Remedios Cipriano de la Santísima Trinidad Ruiz y Picasso was born in Malaga, Spain, in 1881. Ruiz was his father’s family name and Picasso his mother’s--the reason painter Pablo chose the latter will become clear in a moment. At the age of fourteen, Picasso’s family moved to Corunna and then Barcelona. At sixteen, he was entirely on his own, living alone in Madrid, and at eighteen, he made his first trip to Paris, moving there permanently in 1904. Thereafter, France was Picasso’s adopted home. A prodigy is something outside the bounds of nature, and Picasso was certainly that. Family members said that he could draw before he could talk (Einstein was also a late talker). The first word he uttered was piz, his baby word for lapiz (pencil). When he wanted something, he would simply draw it as, for example, “the long, twisting, sugar-dusted fritters one buys hot from stalls all over Spain.” As a painter, Picasso had a natural advantage, as would a musician with perfect pitch. Imagine that you are that one person in 10,000 who can instantly and accurately identify any musical pitch. You can also go to the piano and reproduce the melody of a tune at pitch on only one hearing. Already you have a head start in your profession. Similarly, Picasso seems to have had a “perfect eye” for drawing. This sort of eye-to-hand duplicative ability is genetic and cannot be taught—anymore than absolute pitch can be taught. It comes immediately and effortlessly. Moreover, like Mozart, Picasso had the ability to “see” a work of art in his mind--if not fully formed, then at least in most of its particulars. This gift of conjuring--instantaneous conceptual thinking--stayed with him until the very end. A rebellious resistance to formal education seems only to have enhanced Picasso’s natural gifts. The more the father pushed for conventional learning, the more the boy pushed back toward the art he loved. In class, young Picasso was disruptive, preferring to go to the window sill, look out, and draw. According to his lifelong friend Jaime Sabartés: “He displayed only the profoundest indifference, especially toward words and numbers. He wanted only to scribble on all the papers on which he could lay his hands, to copy . . . everything he saw.” Picasso was no Einstein--but Einstein was no Picasso. Einstein played chess and Mozart’s sonatas on his violin; Picasso played dominoes and listened to guitar music in cafés. Genius follows more than one muse. As with most geniuses, Picasso learned not formally, but intuitively. Picasso also had, for better or for worse, a mentor: his father, José Ruiz y Blasco. José Ruiz was a painter whose one claim to fame was his capacity to depict pigeons. According to son Pablo, Don José had little patience with the most detailed part of the job, the feet, and these became the task of the son. “My father would cut off the legs of a dead pigeon and pin them down on a board, in a convenient position, and I would copy them minutely, until they met with his approval.” Eventually, when Picasso was about age fourteen, “He gave me his paints and his brushes, and never went back to painting.” The incompetence of father Picasso, however, bestowed a gift upon the son—the foundation of a craft. More to his liking was the time Picasso spent in Madrid where he studied, not from professors in the academy to which he had been sent, but rather at the feet of the great masters in the Prado Museum, copying the works of Velasquez, Zubaran, and Goya. Vivaldi was copied by Bach, Bach by Mozart, Mozart by Beethoven, and Beethoven by Wagner. The great ones always learn their craft—but on their own. What does the word uttered mean as it is used in the passage?