table of limits

简明释义

限额表

英英释义

例句

1.To avoid any compliance issues, the manufacturer always consults the table of limits before production.

为了避免任何合规问题，制造商在生产前总是咨询限制表。

2.The engineer referred to the table of limits to ensure the dimensions were within specifications.

工程师参考了限制表以确保尺寸在规范范围内。

3.Before finalizing the design, the team checked the table of limits for material tolerances.

在最终确定设计之前，团队检查了材料公差的限制表。

4.The table of limits provided essential data for quality control during production.

生产过程中，限制表提供了重要的数据用于质量控制。

5.In the lab, the researcher used the table of limits to determine the acceptable range for experimental results.

在实验室，研究人员使用限制表来确定实验结果的可接受范围。

作文

In the realm of mathematics and science, the concept of limits plays a crucial role in understanding various phenomena. One particular term that encapsulates this idea is the table of limits, which serves as a valuable resource for students and professionals alike. A table of limits is essentially a compilation of standard limits that are frequently encountered in calculus and analysis. This table provides quick reference points for evaluating limits of functions as they approach specific values or infinity. The importance of a table of limits cannot be overstated. For students learning calculus, it acts as a foundational tool that aids in grasping the behavior of functions. Understanding limits is vital for mastering more advanced topics such as derivatives and integrals. The table of limits allows students to quickly identify common limits without having to derive them from first principles every time. For example, it might include limits such as \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) or \(\lim_{x \to \infty} (1 + \frac{1}{x})^x = e\). These results are not only fundamental but also frequently utilized in various mathematical applications.Moreover, the table of limits is not just beneficial for students; it is also an essential tool for professionals in fields such as engineering, physics, and economics. In these disciplines, limits are often used to model real-world situations. For instance, engineers may use limits to analyze the behavior of structures under different loads, while economists might apply limit concepts to understand market behaviors at equilibrium. Having a reliable table of limits at hand can significantly streamline calculations and improve efficiency in problem-solving.However, while a table of limits is incredibly useful, it is important for students and professionals to not rely solely on it. Understanding the underlying principles of limits is crucial for truly mastering the subject. The table of limits should be seen as a supplementary tool rather than a crutch. By studying the derivation of these limits and practicing their application in various scenarios, individuals can deepen their comprehension and enhance their analytical skills.In conclusion, the table of limits is an invaluable asset in the fields of mathematics and science. It provides quick access to commonly used limits, facilitating learning and application in various contexts. Nonetheless, it is essential to pair this resource with a solid understanding of the principles of limits to ensure a well-rounded mastery of the subject. As students and professionals continue to engage with these concepts, the table of limits will remain a steadfast companion in their mathematical journey.

在数学和科学领域，极限的概念在理解各种现象中起着至关重要的作用。一个特别的术语概括了这一思想，那就是极限表，它为学生和专业人士提供了宝贵的资源。极限表本质上是一个标准极限的汇编，这些极限在微积分和分析中经常遇到。该表为评估函数在接近特定值或无穷大时的极限提供了快速参考点。极限表的重要性不容小觑。对于学习微积分的学生来说，它作为一种基础工具，有助于掌握函数的行为。理解极限对于掌握更高级的主题如导数和积分至关重要。极限表使学生能够快速识别常见的极限，而无需每次都从基本原理推导它们。例如，它可能包括极限如\(\lim_{x \to 0} \frac{\sin x}{x} = 1\)或\(\lim_{x \to \infty} (1 + \frac{1}{x})^x = e\)。这些结果不仅是基础，而且在各种数学应用中也经常使用。此外，极限表不仅对学生有益；它也是工程、物理和经济等领域专业人士的重要工具。在这些学科中，极限常用于建模现实世界的情况。例如，工程师可能会使用极限来分析结构在不同载荷下的行为，而经济学家可能会应用极限概念来理解市场在均衡时的行为。拥有一个可靠的极限表可以显著简化计算并提高解决问题的效率。然而，虽然极限表非常有用，但学生和专业人士不应仅仅依赖于它。理解极限的基本原理对于真正掌握这个主题至关重要。极限表应被视为一种补充工具，而不是拐杖。通过研究这些极限的推导，并在各种场景中练习其应用，个人可以加深理解并增强分析能力。总之，极限表在数学和科学领域是一个无价的资产。它提供了对常用极限的快速访问，促进了在各种背景下的学习和应用。然而，结合对极限原理的扎实理解，确保对该主题的全面掌握是至关重要的。随着学生和专业人士继续参与这些概念，极限表将始终成为他们数学旅程中的坚定伴侣。