limiting value

简明释义

极限值

英英释义

例句

1.The limiting value of pH in this chemical process is crucial for optimal reaction rates.

在这个化学过程中，pH的极限值对最佳反应速率至关重要。

2.The limiting value for temperature in this experiment is set at 100 degrees Celsius to ensure safety.

在这个实验中，温度的极限值设定为100摄氏度，以确保安全。

3.In engineering, the limiting value of stress determines the maximum load a material can withstand before failure.

在工程学中，极限值的应力决定了材料在失效之前可以承受的最大负载。

4.When designing a circuit, engineers must consider the limiting value of current to prevent overheating.

在设计电路时，工程师必须考虑电流的极限值以防止过热。

5.In financial modeling, the limiting value of investment return helps assess risk.

在财务建模中，投资回报的极限值有助于评估风险。

作文

In the realm of mathematics and physics, the concept of a limiting value (极限值) plays a crucial role in understanding various phenomena. A limiting value is essentially the value that a function or sequence approaches as the input or index approaches some value. This idea is foundational for calculus and is used extensively in the study of limits, continuity, and even in real-world applications such as engineering and economics.To illustrate the significance of limiting values (极限值), consider the example of a simple mathematical function, such as f(x) = 1/x. As x approaches infinity, the value of f(x) approaches zero. Thus, we can say that the limiting value of f(x) as x approaches infinity is 0. This example highlights how a function can behave in a predictable manner as it nears a certain point, providing insights into its overall behavior.In physics, limiting values (极限值) are often encountered when examining the behavior of objects under extreme conditions. For instance, in thermodynamics, we might study the limiting value of temperature as a system approaches absolute zero. At this point, the motion of particles theoretically comes to a halt, illustrating a significant limiting value in the field of physics. Understanding these limiting values (极限值) helps scientists predict the behavior of systems and design experiments accordingly.Moreover, in economics, the concept of a limiting value (极限值) can be applied to understand market trends and consumer behavior. For example, as the price of a product decreases, the quantity demanded typically increases until it reaches a certain saturation point. This saturation point can be seen as a limiting value where further decreases in price do not significantly affect demand. Analyzing these limiting values (极限值) allows economists to make informed predictions about market dynamics and consumer preferences.The importance of limiting values (极限值) extends beyond theoretical applications; they are also vital in practical scenarios. Engineers, for instance, must consider limiting values when designing structures to ensure safety and stability. Knowing the maximum load a bridge can bear before failure occurs is essential for preventing catastrophic incidents. Therefore, understanding limiting values (极限值) is not just an academic exercise but a matter of real-world importance.In conclusion, the concept of a limiting value (极限值) is fundamental across various fields, including mathematics, physics, and economics. It provides a framework for understanding how functions behave under specific conditions and aids in predicting outcomes in real-world applications. By grasping the significance of limiting values (极限值), we can enhance our analytical skills and apply this knowledge to solve complex problems in diverse disciplines. Whether in the classroom or in professional settings, the ability to identify and utilize limiting values (极限值) is an invaluable asset that fosters critical thinking and informed decision-making.

在数学和物理的领域中，limiting value（极限值）这一概念在理解各种现象方面扮演着至关重要的角色。limiting value本质上是一个函数或序列在输入或索引接近某个值时所趋近的值。这个理念是微积分的基础，并在极限、连续性研究及甚至工程和经济学等现实应用中被广泛使用。为了说明limiting values（极限值）的重要性，考虑一个简单的数学函数的例子，如f(x) = 1/x。当x接近无穷大时，f(x)的值接近于零。因此，我们可以说f(x)在x接近无穷大时的limiting value是0。这个例子突显了一个函数在接近某个点时可以表现出可预测的行为，从而提供对其整体行为的洞察。在物理学中，limiting values（极限值）常常在研究物体在极端条件下的行为时遇到。例如，在热力学中，我们可能会研究系统在接近绝对零度时的limiting value。在这一点上，粒子的运动理论上会停止，展示了物理学中一个重要的limiting value。理解这些limiting values（极限值）帮助科学家预测系统的行为并相应地设计实验。此外，在经济学中，limiting value（极限值）的概念可以用于理解市场趋势和消费者行为。例如，当某产品的价格降低时，需求量通常会增加，直到达到某个饱和点。这个饱和点可以视为一个limiting value，在此情况下进一步降低价格不会显著影响需求。分析这些limiting values（极限值）使经济学家能够对市场动态和消费者偏好做出明智的预测。limiting values（极限值）的重要性超越了理论应用；它们在实际情境中同样至关重要。工程师在设计结构时必须考虑limiting values以确保安全和稳定。了解一座桥梁在失效前能承受的最大负载对于防止灾难性事件至关重要。因此，理解limiting values（极限值）不仅仅是学术练习，而是现实世界的重要事项。总之，limiting value（极限值）这一概念在数学、物理和经济学等多个领域中都是基础性的。它为理解函数在特定条件下的行为提供了框架，并有助于预测现实应用中的结果。通过掌握limiting values（极限值）的重要性，我们可以增强分析能力，并将这一知识应用于解决各个学科中的复杂问题。无论是在课堂上还是在专业环境中，识别和利用limiting values（极限值）的能力都是一种宝贵的资产，促进了批判性思维和明智的决策制定。