Tính các giới hạn sau: limx→-∞ x2 – 11 – 2x5x7 + x +3 – 2023 – Lam van hay

Tính các giới hạn sau: limx→-∞ x2 – 11 – 2x5x7 + x +3 – 2023

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Post published:18/04/2023
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Câu hỏi:

Cho khoảng K, $x_{0} \in K$ và hàm số y = f(x) xác định trên $K \ \{x_{0}\}$ Chứng minh rằng nếu $\lim x \to x_{0} f (x) = + \infty$ thì luôn tồn tại ít nhất một số c thuộc sao cho f(c) > 0

Trả lời:

Vì Giải sách bài tập Toán 11 | Giải sbt Toán 11

nên với dãy số $(x_{n})$ bất kì, $x_{n} \in K \ \{x_{0}\}$ và $x_{n} \to x_{0}$ ta luôn có Từ định nghĩa suy ra $f (x_{n})$ có thể lớn hơn một số dương bất kì, kể từ một số hạng nào đó trở đi.Nếu số dương này là 1 thì $f (x_{n}) > 1$ kể từ một số hạng nàođó trởđi.Nói cách khác, luôn tồn tạiít nhất một số $x_{k} \in K \ \{x_{0}\}$ sao cho $f (x_{k}) > 1$ .

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Read the passage and mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions. Dark matter in the universe is believed by some scientists to be a substance that is not readily observable because it does not directly refract light or energy. Its existence can only be deduced because of the effect that it has on surrounding matter. In fact, some members of the scientific community have argued that dark matter does not actually exist. Others, however, believe in its existence, in part because the scientific community does not have a complete understanding of gravita science. On the other hand, some would argue that it is the understanding of gravitational science that leads most scientists to believe in the existence of dark matter, because without dark matter, there are many cosmological phenomena that are difficult to explain. For example, dark matter in the universe may have a peculiar effect on the Milky Way galaxy. Some scientists believe that the interaction between dark matter and other smaller, nearby galaxies is causing the Milky Way galaxy to take on a warped profile. It has been asserted that not only does dark matter exist, it may also be responsible for the Milky Way’s unusual shape. The interaction referenced involves two smaller galaxies near the Milky Way, called Magellanic clouds, moving through an enormous amount of dark matter, which, in effect, enhances the gravitational pull that the two Magellanic clouds could have on the Milky Way and other surrounding bodies. Without the existence of the dark matter, the Magellanic clouds would not have sufficient mass to have such a strong effect on the bend of the Milky Way galaxy. The strongest evidence for the validity of this hypothesis rests in Newtonian physics, and the hypothesis that anything with mass will exert a gravitational pull. The Milky Way and other galaxies with peculiar warped shapes are being molded by a gravitational force. However, there is nothing readily observable with sufficient mass that could cause such a high level of distortion via gravitational pull in the vicinity of the Milky Way. Therefore, something that is not easily observed must be exerting the necessary force to create the warped shape of the galaxy. Aaron Romanowsky and several colleagues have questioned the effect that dark matter might have on galaxies. They point to the existence of several elliptical galaxies surrounded by very little dark matter as evidence that dark matter is not, in fact, the cause of the warped galaxies. While they do not claim that their findings should be interpreted to conclude that dark matter does not exist, they apparently believe that the results of their studies cast doubt on some of the conventional theories of galaxy formation and manipulation. Several models constructed by researchers from the University of California at Berkeley, however, point to the idea that dark matter is the most likely explanation for the distorted shape of the Milky Way and other galaxies. Using computer models, they have mapped the likely interactions between certain galaxies and the surrounding dark matter, and those models have shown not only the possibility that dark matter is responsible for the warped shape of the Milky Way, but that the relationship between the dark matter and the Magellanic clouds is dynamic; the movement of the clouds through the dark matter seems to create a wake that enhances their gravitational influence on the Milky Way. What does the passage offer as evidence for the existence of dark matter? – 2023

25/04/2023

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