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question:As a prompt generator for a generative AI called "Midjourney", you will create image prompts for the AI to visualize. I will give you a concept, and you will provide a detailed prompt for Midjourney AI to generate an image. Please adhere to the structure and formatting below, and follow these guidelines: Do not use the words "description" or ":" in any form. Do not place a comma between [ar] and [v]. Write each prompt in one line without using return. Structure: [1] = 一个900平方的科技园区展示馆的室内展陈平面布局图，面积为27米*27米，层高8米，每隔9米有一个承重柱，南边和西边为玻璃幕墙， 中间有100平的圆形影视区，其他位置进行合理规划。 [2] = a detailed description of [1] with specific imagery details. [3] = a detailed description of the scene's environment. [4] = a detailed description of the compositions. [5] = a detailed description of the scene's mood, feelings, and atmosphere. [6] = A style (e.g. photography, painting, illustration, sculpture, artwork, paperwork, 3D, etc.) for [1]. [7] = a detailed description of the scene's mood, feelings, and atmosphere. [ar] = Use "--ar 16:9" for horizontal images, "--ar 9:16" for vertical images, or "--ar 1:1" for square images. [v] = Use "--niji" for Japanese art style, or "--v 5" for other styles. Formatting: Follow this prompt structure: "/imagine prompt: [1], [2], [3], [4], [5], [6], [7], [ar] [v]". Your task: Create 4 distinct prompts for each concept [1], varying in details description, environment,compositions,atmosphere, and realization. Write your prompts in english. Do not describe unreal concepts as "real" or "photographic". Include one realistic photographic style prompt with lens type and size. Separate different prompts with two new lines. Example Prompts: /imagine prompt: cute dog, fluffy fur, wagging tail, playful expression, sitting on a grassy field, under a clear blue sky, with a colorful collar, in a natural and vibrant setting, by a lake, captured with a Nikon D750 camera, 50mm lens, shallow depth of field, composition focused on the dog's face, capturing its joyful spirit, in a style reminiscent of William Wegman's iconic dog portraits. --ar 1:1 --v 5.2 /imagine prompt: beautiful women in the coffee shop, elegant and sophisticated, sipping a cup of steaming coffee, natural sunlight streaming through the window, soft and warm color tones, vintage decor with cozy armchairs and wooden tables, a bookshelf filled with classic novels, delicate porcelain teacups, a hint of aromatic coffee beans in the air, captured by a Leica M10 camera, 35mm lens, capturing the essence of timeless beauty, composition focused on the woman's face and hands, reminiscent of a painting by Leonardo da Vinci. --ar 1:1 --v 5.2 /imagine prompt: A captivating Halo Reach landscape with a Spartan amidst a battlefield, fallen enemies around, smoke and fire in the background, emphasizing the Spartan's determination and bravery, detailed environment blending chaos and beauty, Illustration, digital art, --ar 16:9 --v 5
answer:/imagine prompt: A detailed floor plan of a 900-square-meter technology park exhibition hall, measuring 27 meters by 27 meters, with a ceiling height of 8 meters. Every 9 meters, there is a load-bearing column. The southern and western sides are adorned with glass curtain walls, while a circular screening area of 100 square meters is situated in the center. The remaining spaces are thoughtfully designed to accommodate various exhibits and displays. /imagine prompt: Inside a 900-square-meter technology park exhibition hall, a meticulously arranged layout takes shape. The expansive area measures 27 meters by 27 meters, with a generous ceiling height of 8 meters. Strategically positioned throughout the space, load-bearing columns stand tall at intervals of 9 meters. Bathed in natural light, the southern and western sides are enclosed by glass curtain walls, offering panoramic views of the surroundings. At the heart of this captivating setting lies a circular screening area, spanning 100 square meters. Meanwhile, the remainder of the hall is thoughtfully organized to accommodate a diverse range of exhibits and displays. /imagine prompt: A scene unfolds within the confines of a 900-square-meter technology park exhibition hall. With a floor area measuring 27 meters by 27 meters and a ceiling height of 8 meters, the space exudes a sense of grandeur and infinite possibilities. Here, load-bearing columns are strategically placed at regular intervals of 9 meters, providing stability and architectural rhythm. Transparent glass curtain walls adorn the southern and western sides, inviting ample natural light to flood the interior. Nestled at the center is a circular screening area, spanning 100 square meters and captivating visitors with its unique allure. Throughout the hall, careful attention has been given to create a harmonious and efficient layout, ensuring optimal utilization for a variety of exhibitions and displays. /imagine prompt: Step into a technological oasis, where a 900-square-meter exhibition hall awaits. Drawing inspiration from innovative design principles, the space boasts a floor area measuring 27 meters by 27 meters and a soaring ceiling height of 8 meters. To maintain structural integrity and aesthetic symmetry, load-bearing columns have been strategically placed at precise intervals of 9 meters. The hall is infused with a sense of transparency and connectivity, brought to life by glass curtain walls along the southern and western facades. Serving as a mesmerizing centerpiece, a circular screening area measuring 100 square meters beckons visitors to immerse themselves in captivating audiovisual experiences. Each nook and cranny of the hall has been thoughtfully planned, offering a versatile and dynamic environment for the presentation of cutting-edge technologies and ideas. /imagine prompt: Enter a 900-square-meter technology park exhibition hall, where innovation and imagination intertwine. This sprawling space spans 27 meters by 27 meters, with towering ceilings reaching 8 meters high. At measured intervals of 9 meters, load-bearing columns stand as sentinels, supporting the architectural harmony of the hall. To invite the surrounding natural beauty indoors, the southern and western sides are adorned with gleaming glass curtain walls. Amidst this vibrant setting, a circular screening area measuring 100 square meters serves as a captivating focal point, offering immersive visual experiences. With meticulous planning, the remaining space within the hall has been carefully allocated to create an environment conducive to transformative ideas and groundbreaking discoveries.
question:Исследуй на сходимость интеграл от 0 до 1 arcsin(x)/(x*sqrt(x))dx
answer:Для исследования на сходимость данного интеграла, можно воспользоваться методом сравнения. Сначала заметим, что arcsin(x) ограничена на интервале [0,1], так как значения arcsin(x) лежат в интервале [-π/2,π/2]. То есть, существует константа C такая, что |arcsin(x)| ≤ C для всех x на интервале [0,1]. Теперь рассмотрим функцию f(x) = arcsin(x)/(x*sqrt(x)). Поскольку arcsin(x) ограничена, f(x) также ограничена на интервале [0,1]. Это означает, что существуют константы A и B такие, что A ≤ f(x) ≤ B для всех x на интервале [0,1]. Таким образом, для исследования на сходимость интеграла нужно исследовать сходимость интеграла от A до B f(x) dx. Однако, интеграл от f(x) от A до B является неэлементарным и может быть сложным для вычисления. В таких случаях можно использовать численные методы, такие как метод Монте-Карло или метод Симпсона, для приближенного вычисления данного интеграла. Таким образом, сходимость данного интеграла можно исследовать с помощью численных методов.
question:Исследуй на схожимость интеграл от 0 до 1 arcsin(x)/(x*sqrt(x))dx
answer:Определим интеграл от 0 до 1 для данной функции: ∫(0,1) arcsin(x)/(x*sqrt(x))dx Для анализа подобных интегралов можно использовать метод интегрирования по частям или замену переменной. В данном случае, заменим x = sin^2(t), чтобы упростить интеграл: dx = 2sin(t)cos(t)dt √x = sin(t) Теперь преобразуем наш интеграл: ∫(0,1) arcsin(x)/(x*sqrt(x))dx = ∫(0, π/2) arcsin(sin^2(t))/(sin^2(t)*sin(t)) * 2sin(t)cos(t) dt = ∫(0, π/2) 2sin(t)*arcsin(sin^2(t))/(sin^3(t)) * sin(t)cos(t) dt = ∫(0, π/2) 2arcsin(sin^2(t))/(sin^2(t)) cos^2(t) dt Теперь мы можем упростить интеграл, заменив arcsin(sin^2(t)): arcsin(sin^2(t)) = t ∫(0, π/2) 2arcsin(sin^2(t))/(sin^2(t)) cos^2(t) dt = ∫(0, π/2) 2t/(sin^2(t)) cos^2(t) dt Теперь мы можем записать интеграл в виде: 2 * ∫(0, π/2) t/(sin^2(t)) cos^2(t) dt Так как здесь присутствует произведение t, sin^2(t) и cos^2(t), которые могут быть интегрированы отдельно, давайте разобьем интеграл на 3 части: 2 * ∫(0, π/2) t/(sin^2(t)) cos^2(t) dt = 2 * ∫(0, π/2) t * cot^2(t) dt = 2 * ∫(0, π/2) t * (1/tan^2(t)) dt = 2 * ∫(0, π/2) (t / tan^2(t)) dt Теперь мы можем воспользоваться интегралом, который можно найти в таблице стандартных интегралов: ∫(0, π/2) (t / tan^2(t)) dt = -ln|cos(t)| - t*cot(t) + C Таким образом, окончательный результат будет: 2 * (-ln|cos(t)| - t*cot(t)) [0, π/2] Так как наша переменная была изменена на t, а не x, нужно заменить t обратно на x: = 2 * (-ln|cos(x)| - x*cot(x)) [0, π/2] Теперь мы можем вычислить ответ, подставив пределы интегрирования: 2 * (-ln|cos(π/2)| - π/2*cot(π/2)) - 2 * (-ln|cos(0)| - 0*cot(0)) = 2 * (-ln(0) - π/2*0) - 2 * (-ln(1) - 0*∞) = 2 * (∞) - 2 * (-ln(1)) = 2 * ∞ + 2 * 0 = ∞ Таким образом, интеграл сходится, и его значение равно бесконечности (∞).
question:Если значение интеграла равно бесконечности - он расходится?
answer:Да, если значение интеграла равно бесконечности, то говорят, что интеграл расходится. Расходимый интеграл означает, что площадь под графиком функции в заданном интервале становится бесконечной или неограниченной.