limit value

简明释义

极限值

英英释义

例句

1.The software has a limit value for data input to prevent overflow errors.

该软件对数据输入有一个限制值以防止溢出错误。

2.The engineer set the limit value for the temperature to avoid equipment damage.

工程师设定了温度的限制值以避免设备损坏。

3.In the experiment, we need to ensure that the limit value of the pH level is maintained.

在实验中，我们需要确保限制值得到维持。

4.The limit value for noise levels in residential areas is strictly enforced by local laws.

住宅区的噪音水平的限制值受到当地法律的严格执行。

5.During the audit, the accountant noted that the limit value for expenses had been exceeded.

在审计过程中，会计注意到费用的限制值已被超过。

作文

In the realm of mathematics and science, the concept of limit value (极限值) plays a pivotal role in understanding various phenomena. A limit value refers to the value that a function approaches as the input approaches a certain point. This is particularly important in calculus, where it helps in determining the behavior of functions at specific points, especially when they are not defined or exhibit indeterminate forms.To illustrate the significance of limit value (极限值), let us consider the function f(x) = (x^2 - 1)/(x - 1). At first glance, if we substitute x = 1 into the function, we encounter an indeterminate form of 0/0. However, by factoring the numerator, we can rewrite the function as f(x) = (x + 1) when x is not equal to 1. As x approaches 1, the function approaches a limit value of 2. This example highlights how limit values allow us to evaluate functions that otherwise seem undefined at certain points.The application of limit values extends beyond pure mathematics into fields such as physics and engineering. For instance, in physics, the concept of velocity is often derived from the limit value of the average speed as the time interval approaches zero. This leads to the definition of instantaneous velocity, which is crucial for understanding motion. Similarly, in engineering, limit values are used in the analysis of materials, where engineers must determine the maximum stress a material can withstand before failure.Moreover, limit values (极限值) are integral to the study of sequences and series. In this context, a sequence may converge to a particular limit value, indicating that as the terms of the sequence progress, they get arbitrarily close to a specific number. This notion of convergence is essential in various applications, including numerical methods, where approximations are made to reach a desired accuracy.In practical terms, understanding limit values enables scientists and mathematicians to make predictions and solve complex problems. For example, in economics, the concept of marginal cost is derived from the limit value of total cost as production quantity changes. This insight allows businesses to optimize production levels and maximize profits.In conclusion, the concept of limit value (极限值) is fundamental across multiple disciplines. It provides a framework for analyzing and understanding the behavior of functions, sequences, and real-world phenomena. By mastering the idea of limit values, students and professionals alike can unlock new insights and enhance their problem-solving skills. The ability to compute and interpret limit values is not only an academic exercise but also a vital tool in various scientific and practical applications, making it an essential component of a well-rounded education in mathematics and the sciences.

在数学和科学领域，极限值（limit value）的概念在理解各种现象中起着关键作用。极限值指的是当输入接近某一点时，函数所趋近的值。这在微积分中尤为重要，因为它有助于确定函数在特定点的行为，尤其是在这些点未定义或表现出不确定形式时。为了说明极限值的重要性，让我们考虑函数f(x) = (x^2 - 1)/(x - 1)。乍一看，如果我们将x = 1代入这个函数，我们会遇到一个不确定形式0/0。然而，通过对分子进行因式分解，我们可以将函数重写为f(x) = (x + 1)，当x不等于1时。当x接近1时，函数趋近于极限值2。这个例子突显了极限值如何让我们评估在某些点看似未定义的函数。极限值的应用超越了纯数学，延伸到物理学和工程学等领域。例如，在物理学中，速度的概念通常是通过当时间间隔趋近于零时的平均速度的极限值得出的。这导致了瞬时速度的定义，这对于理解运动至关重要。同样，在工程学中，极限值被用于材料分析，工程师必须确定材料在失效之前能够承受的最大应力。此外，极限值（limit value）是序列和级数研究中的重要组成部分。在这种情况下，一个序列可能收敛到一个特定的极限值，这表明随着序列项的进展，它们越来越接近某个特定的数字。这种收敛的概念在各种应用中至关重要，包括数值方法，在这些方法中，进行近似以达到所需的精度。从实际角度来看，理解极限值使科学家和数学家能够做出预测并解决复杂问题。例如，在经济学中，边际成本的概念是通过生产数量变化时总成本的极限值得出的。这一见解使企业能够优化生产水平并最大化利润。总之，极限值（limit value）这一概念在多个学科中都是基础。它提供了分析和理解函数、序列和现实世界现象行为的框架。通过掌握极限值的概念，学生和专业人士都可以解锁新的见解，并增强他们的问题解决能力。计算和解释极限值的能力不仅是一种学术练习，也是各种科学和实际应用中的重要工具，使其成为数学和科学教育中不可或缺的组成部分。