limiting value

简明释义

极限值

英英释义

例句

1.In economics, the limiting value of demand can affect pricing strategies.

在经济学中，需求的极限值可能会影响定价策略。

2.The limiting value of a function as it approaches infinity can help determine its end behavior.

当一个函数趋近于无穷大时，其极限值可以帮助确定其末端行为。

3.In physics, the concept of a limiting value is crucial for understanding asymptotic behavior.

在物理学中，极限值的概念对于理解渐近行为至关重要。

4.The engineer calculated the limiting value for stress in the material to ensure safety.

工程师计算了材料的极限值以确保安全。

5.In statistics, the limiting value of a sample mean can provide insights into population parameters.

在统计学中，样本均值的极限值可以为总体参数提供见解。

作文

In the realm of mathematics and science, the concept of a limiting value is crucial for understanding various phenomena. A limiting value refers to the value that a function or sequence approaches as the input or index approaches some value. This idea is not only fundamental in calculus but also plays a significant role in real-world applications such as physics, engineering, and economics.To illustrate this concept, consider the example of a simple mathematical function, f(x) = 1/x. As x approaches infinity, the value of f(x) approaches zero. In this case, we can say that the limiting value of f(x) as x approaches infinity is 0. This example shows how a function can get closer and closer to a specific value without necessarily reaching it. Understanding limiting values helps mathematicians and scientists predict behaviors and outcomes in various situations.In physics, the concept of limiting value can be seen in the study of motion. For instance, when an object falls under the influence of gravity, its velocity increases until it reaches a point where air resistance balances the gravitational force. At this point, the object stops accelerating and continues to fall at a constant speed known as terminal velocity. Here, terminal velocity acts as a limiting value for the object's speed. Recognizing this limiting value allows engineers to design safer vehicles and structures by accounting for forces acting on them.Furthermore, in economics, the limiting value can be observed in supply and demand models. When the price of a good rises, the quantity supplied generally increases while the quantity demanded decreases. However, there comes a point where the price cannot increase indefinitely due to market saturation or consumer preferences. This maximum price that consumers are willing to pay becomes a limiting value for the market. By analyzing these limiting values, economists can make informed predictions about market behavior and potential interventions.In conclusion, the concept of a limiting value is vital across various fields of study. It provides a framework for understanding how functions behave, how physical systems operate, and how markets respond to changes. By grasping the significance of limiting values, students and professionals can enhance their analytical skills and apply these concepts to solve real-world problems. The ability to identify and work with limiting values empowers individuals to make better decisions, whether in scientific research, engineering projects, or economic strategies. As we continue to explore the complexities of the world around us, the understanding of limiting values will undoubtedly remain a cornerstone of our intellectual endeavors.

在数学和科学领域，极限值的概念对于理解各种现象至关重要。极限值指的是当输入或索引接近某个值时，函数或序列所趋近的值。这个概念不仅在微积分中是基础，在物理学、工程学和经济学等现实应用中也起着重要作用。为了说明这一概念，考虑一个简单的数学函数f(x) = 1/x。当x趋近于无穷大时，f(x)的值趋近于零。在这种情况下，我们可以说f(x)在x趋近于无穷大时的极限值是0。这个例子展示了一个函数可以越来越接近某个特定值，而不一定达到它。理解极限值帮助数学家和科学家预测各种情况的行为和结果。在物理学中，极限值的概念可以在运动研究中看到。例如，当一个物体在重力影响下自由下落时，其速度会增加，直到达到一个点，此时空气阻力与重力平衡。此时，物体停止加速，并以一个恒定的速度继续下落，这个速度被称为终端速度。在这里，终端速度充当了物体速度的极限值。认识到这个极限值使工程师能够通过考虑作用在车辆和结构上的力量来设计更安全的交通工具和建筑。此外，在经济学中，极限值可以在供需模型中观察到。当一种商品的价格上涨时，供应量通常会增加，而需求量会减少。然而，存在一个点，价格不能无限制地上涨，因为市场饱和或消费者偏好。这种消费者愿意支付的最高价格成为市场的极限值。通过分析这些极限值，经济学家可以对市场行为和潜在干预措施做出明智的预测。总之，极限值的概念在各个学科中都是至关重要的。它为理解函数的行为、物理系统的运作以及市场对变化的反应提供了框架。通过掌握极限值的重要性，学生和专业人士可以增强他们的分析技能，并将这些概念应用于解决现实问题。识别和处理极限值的能力使个人能够在科学研究、工程项目或经济策略中做出更好的决策。随着我们继续探索周围世界的复杂性，理解极限值无疑将继续成为我们智力努力的基石。