limit value; limiting value

简明释义

极限值

英英释义

例句

1.In the context of environmental regulations, the limiting value for air pollutants must be strictly adhered to.

在环境法规的背景下，空气污染物的限制值必须严格遵守。

2.The limit value of this machine's temperature is set at 100 degrees Celsius to prevent overheating.

这台机器的极限值设定在100摄氏度，以防止过热。

3.The limit value for blood alcohol concentration while driving is 0.08% in many countries.

在许多国家，驾驶时血液酒精浓度的极限值为0.08%。

4.The limit value for noise levels in residential areas is usually around 55 decibels.

住宅区的极限值通常在55分贝左右。

5.According to the safety guidelines, the limiting value for exposure to chemicals is crucial for worker health.

根据安全指南，化学品接触的限制值对工人健康至关重要。

作文

In the realm of mathematics and science, the concept of limit value; limiting value plays a crucial role in understanding the behavior of functions and sequences as they approach a certain point. The limit value; limiting value is essentially the value that a function or sequence approaches as the input or index approaches some value. This idea is foundational in calculus, where it helps us analyze continuous functions and their properties. For instance, when we talk about the limit of a function as it approaches a particular x-value, we are often interested in what value the function gets closer to, rather than what it actually equals at that point.Consider the function f(x) = 1/x. As x approaches 0 from the positive side, the values of f(x) become very large. In this case, we say that the limit value; limiting value of f(x) as x approaches 0 is infinity. Conversely, as x approaches 0 from the negative side, the values of f(x) become very large in the negative direction, which illustrates that the function does not have a defined limit at x = 0. This example highlights the importance of understanding limit value; limiting value in determining the behavior of functions near points of discontinuity.The application of limit value; limiting value extends beyond pure mathematics into various fields such as physics, engineering, and economics. For instance, in physics, the concept helps describe phenomena like velocity and acceleration. When analyzing motion, we might look at the limit value; limiting value of an object’s position over time to determine its instantaneous velocity. This involves taking the limit of the average velocity as the time interval approaches zero, allowing us to find a precise measurement of speed at a given moment.In engineering, the limit value; limiting value can be essential for understanding stress and strain on materials. Engineers must consider the limits of materials when designing structures to ensure safety and functionality. For example, knowing the limit value; limiting value of tensile strength can help engineers avoid material failure under load. By calculating the limit value; limiting value, they can design components that will withstand expected forces without breaking.Economists also utilize the concept of limit value; limiting value when analyzing market trends and consumer behavior. They often look at the limit value; limiting value of demand as prices change, helping predict how consumers will react to price fluctuations. Understanding these limits allows businesses to strategize pricing effectively, maximizing profit while meeting consumer needs.In conclusion, the concept of limit value; limiting value is integral to various disciplines, providing insight into the behavior of functions, physical systems, and economic models. Whether in mathematics, science, or practical applications, recognizing and calculating limit value; limiting value enables us to make informed decisions and predictions. As we continue to explore these ideas, we deepen our understanding of the world around us and improve our ability to analyze complex situations. Therefore, mastering the concept of limit value; limiting value is not just an academic exercise but a vital skill that enhances our critical thinking and problem-solving capabilities.

在数学和科学领域，极限值；限制值的概念在理解函数和序列在接近某个点时的行为方面发挥着至关重要的作用。极限值；限制值本质上是指函数或序列当输入或索引接近某个值时所接近的值。这个思想在微积分中是基础性的，它帮助我们分析连续函数及其性质。例如，当我们谈论一个函数在某个特定x值附近的极限时，我们通常关注的是函数接近的值，而不是它在该点实际等于的值。考虑函数f(x) = 1/x。当x从正侧接近0时，f(x)的值变得非常大。在这种情况下，我们说f(x)在x接近0时的极限值；限制值是无穷大。相反，当x从负侧接近0时，f(x)的值在负方向上变得非常大，这说明该函数在x = 0时没有定义的极限。这个例子突显了理解极限值；限制值的重要性，以确定函数在不连续点附近的行为。极限值；限制值的应用超越了纯数学，延伸到物理、工程和经济等多个领域。例如，在物理学中，这个概念帮助描述速度和加速度等现象。当分析运动时，我们可能会查看物体位置随时间变化的极限值；限制值，以确定其瞬时速度。这涉及到在时间间隔接近零时计算平均速度的极限，从而使我们能够找到某一时刻的精确速度测量。在工程学中，极限值；限制值对于理解材料的应力和应变至关重要。工程师在设计结构时必须考虑材料的极限，以确保安全和功能性。例如，了解拉伸强度的极限值；限制值可以帮助工程师避免在负载下材料的失效。通过计算极限值；限制值，他们可以设计出能够承受预期力量而不破裂的组件。经济学家在分析市场趋势和消费者行为时也利用极限值；限制值的概念。他们常常观察需求随着价格变化的极限值；限制值，以帮助预测消费者对价格波动的反应。理解这些限制使企业能够有效地制定定价策略，最大化利润，同时满足消费者需求。总之，极限值；限制值的概念对于各个学科都是不可或缺的，为我们提供了对函数、物理系统和经济模型行为的洞察。无论是在数学、科学还是实际应用中，识别和计算极限值；限制值使我们能够做出明智的决策和预测。随着我们继续探索这些思想，我们加深了对周围世界的理解，提高了分析复杂情况的能力。因此，掌握极限值；限制值的概念不仅仅是学术练习，而是一项增强我们批判性思维和解决问题能力的重要技能。