limiting value

简明释义

极限值

英英释义

例句

1.The engineer calculated the limiting value for stress on the bridge to ensure safety.

工程师计算了桥梁的限制值以确保安全。

2.During the experiment, the team observed that the limiting value of temperature affected the results.

在实验过程中，团队观察到温度的限制值影响了结果。

3.In economics, the limiting value of a product's demand can influence pricing strategies.

在经济学中，产品需求的限制值可以影响定价策略。

4.The limiting value of the budget forced the project manager to make tough decisions.

预算的限制值迫使项目经理做出艰难的决定。

5.The scientist determined the limiting value of the reaction rate under specific conditions.

科学家确定了在特定条件下反应速率的限制值。

作文

In the realm of mathematics and science, the concept of a limiting value plays a crucial role in understanding various phenomena. A limiting value refers to a value that a function or sequence approaches as the input or index approaches some value. This idea is fundamental in calculus, particularly when discussing limits, continuity, and convergence. For instance, when we analyze the behavior of a function as it approaches a certain point, we often look for its limiting value. To illustrate this, consider the function f(x) = 1/x. As x approaches infinity, the values of f(x) get closer and closer to 0. Therefore, we can say that the limiting value of f(x) as x approaches infinity is 0. This concept is not only applicable in mathematics but also finds relevance in various fields such as physics, economics, and engineering.In physics, the idea of a limiting value is essential when dealing with concepts like velocity and acceleration. For example, as an object falls freely under the influence of gravity, its velocity increases until it reaches terminal velocity, which is a limiting value where the force of air resistance equals the gravitational pull on the object. At this point, the object no longer accelerates; instead, it continues to fall at a constant speed. Understanding this limiting value helps physicists predict the motion of falling objects accurately.Economics also utilizes the concept of limiting value when analyzing market trends and consumer behavior. For instance, the demand for a product may increase as its price decreases, but there comes a point where further price reductions will not significantly boost demand. This point can be considered a limiting value for demand concerning price. Recognizing these limiting values enables businesses to make informed decisions about pricing strategies and inventory management.Moreover, in engineering, the limiting value is crucial when designing structures and systems. Engineers must consider the maximum load a bridge can sustain before failure occurs. This maximum load is essentially a limiting value that ensures safety and reliability in construction. By understanding these limiting values, engineers can create designs that withstand various stresses and strains, ultimately leading to safer infrastructures.In conclusion, the concept of a limiting value is integral to many disciplines, providing insights into the behavior of functions, physical systems, economic models, and engineering designs. Whether it is in mathematics, physics, economics, or engineering, recognizing and understanding limiting values allows professionals to make more accurate predictions and informed decisions. As we continue to explore these fields, the importance of limiting values remains evident, highlighting the interconnectedness of knowledge and the significance of mathematical principles in our everyday lives.

在数学和科学领域，limiting value（极限值）这一概念对于理解各种现象至关重要。limiting value指的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。这个思想在微积分中是基本的，特别是在讨论极限、连续性和收敛性时。例如，当我们分析一个函数在接近某个点时的行为时，我们通常会寻找它的limiting value。为了说明这一点，考虑函数f(x) = 1/x。当x接近无穷大时，f(x)的值越来越接近于0。因此，我们可以说f(x)在x接近无穷大时的limiting value是0。这个概念不仅适用于数学，还在物理学、经济学和工程学等多个领域中具有相关性。在物理学中，limiting value的概念在处理速度和加速度等概念时至关重要。例如，当一个物体在重力作用下自由下落时，其速度会增加，直到达到终端速度，这是一种limiting value，在此点上空气阻力的作用力等于物体的重力。此时，物体不再加速，而是以恒定速度继续下落。理解这个limiting value有助于物理学家准确预测下落物体的运动。经济学也利用limiting value这一概念来分析市场趋势和消费者行为。例如，某种产品的需求可能会随着其价格的降低而增加，但到了某个点，进一步的降价不会显著提升需求。这个点可以被视为需求相对于价格的limiting value。识别这些limiting values使企业能够对定价策略和库存管理做出明智的决策。此外，在工程学中，limiting value在设计结构和系统时至关重要。工程师必须考虑桥梁在发生故障前所能承受的最大负荷。这个最大负荷本质上就是一个limiting value，确保了建筑的安全性和可靠性。通过理解这些limiting values，工程师可以创建能够承受各种压力和应变的设计，最终导致更安全的基础设施。总之，limiting value的概念在许多学科中都是不可或缺的，为函数、物理系统、经济模型和工程设计的行为提供了深入的见解。无论是在数学、物理学、经济学还是工程学，识别和理解limiting values使专业人士能够做出更准确的预测和明智的决策。随着我们继续探索这些领域，limiting values的重要性仍然显而易见，突显了知识的相互联系以及数学原理在我们日常生活中的重要性。