asymptote

简明释义

英[ˈeɪsɪmptəʊt]美[ˈæsɪmˌtoʊt]

n. [数] 渐近线

英英释义

单词用法

同义词

反义词

例句

1.You need to find vertical asymptote first.

你需要先找到垂直渐进线。

2.The critical aspect ratio of the fiber is defined as the crosspoint of the tangent value of the inflexion and the asymptote of the maximum elastic modulus.

将与曲线拐点切线和最大值水平直线交点相对应的长径比值定义为纤维临界长径比，将与此相对应的函数值定义为弹性模量临界值。

3.This article elaborates the solution of asymptote of rational function curve, pointing out both the common way of finding limit value and the elementary way.

文章阐述了求有理函数曲线的渐近线，不仅可用常规的通过求极限值的方法来确定，还可用初等方法来确定。

4.The frequency in the response spectrum where the zero period acceleration asymptote begins.

频率响应谱中的零期渐近开始加速。

5.The results shows that fouling grow curve is representative asymptote. Besides, the fouling growth rate increases while surface temperature increases.

实验结果表明，污垢热阻随时间变化曲线为典型的渐近线型，且随着壁面温度的升高，污垢的结垢速率增加。

6.You can't ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving. — Paul Kalanithi 《When Breath Becomes Air》

你永远无法到达完美的境地，但通过不懈的努力奋斗和追求，你能看见那无限接近完美的渐进曲线。— 保罗·卡拉尼什《当呼吸化为空气》。

7.In calculus, the curve approaches an asymptote 渐近线 but never actually touches it.

在微积分中，曲线接近一个asymptote 渐近线，但从不真正接触它。

8.The graph of the function has a vertical asymptote 渐近线 at x = 3.

该函数的图形在x = 3处有一条垂直的asymptote 渐近线。

9.Understanding asymptotes 渐近线 is crucial for analyzing the behavior of rational functions.

理解asymptotes 渐近线对于分析有理函数的行为至关重要。

10.An asymptote 渐近线 can be horizontal, vertical, or oblique depending on the function.

一个asymptote 渐近线可以是水平的、垂直的或斜的，这取决于函数。

11.As the value of x increases, the function gets closer to the horizontal asymptote 渐近线.

随着x值的增加，函数越来越接近水平的asymptote 渐近线。

作文

In mathematics, an asymptote (渐近线) is a line that a curve approaches as it heads towards infinity. This concept is not only crucial in the field of calculus but also has significant implications in various real-world applications, such as physics, engineering, and economics. Understanding asymptotes (渐近线) can provide deeper insights into the behavior of functions and their graphical representations. To illustrate the idea of asymptotes (渐近线), consider the function f(x) = 1/x. As x approaches infinity, the value of f(x) approaches zero, which means that the x-axis (y=0) acts as a horizontal asymptote (渐近线). Similarly, as x approaches zero from the right, f(x) increases without bound, indicating that there is a vertical asymptote (渐近线) at x=0. These characteristics show how asymptotes (渐近线) can define the limits of a function's behavior. The significance of asymptotes (渐近线) extends beyond pure mathematics. In physics, for instance, the concept of asymptotes (渐近线) can be observed in the study of projectile motion. When analyzing the trajectory of a projectile, one might notice that as the projectile moves further away, its path gets closer to a certain angle but never actually reaches it. This idea can be modeled using asymptotes (渐近线), helping physicists predict the behavior of objects in motion. In engineering, asymptotes (渐近线) play a vital role in understanding the limits of materials and structures. For example, when designing bridges or buildings, engineers must consider the maximum load a structure can bear. The stress-strain curve of materials often approaches a limit, which can be represented by an asymptote (渐近线). Recognizing these limits ensures safety and durability in construction projects. Economics also utilizes the concept of asymptotes (渐近线) in various models. For instance, in the law of diminishing returns, as more resources are added to a production process, the additional output eventually approaches a maximum limit. This behavior can be analyzed using asymptotes (渐近线), allowing economists to understand when it is no longer beneficial to increase input. Furthermore, the graphical representation of functions with asymptotes (渐近线) can reveal critical information about trends and behaviors. By studying these graphs, one can identify key features such as intercepts, turning points, and the overall shape of the function. This visual analysis aids in making informed decisions in various fields, from finance to environmental science. In conclusion, the concept of asymptotes (渐近线) is a fundamental aspect of mathematics that finds applications across numerous disciplines. Whether in calculus, physics, engineering, or economics, understanding asymptotes (渐近线) enhances our comprehension of complex systems and helps us make better predictions about the world around us. By recognizing the significance of asymptotes (渐近线), we can appreciate the intricate relationships between different variables and the limits they impose on our understanding of reality.

在数学中，asymptote（渐近线）是指一条曲线在趋向无穷大时所接近的直线。这个概念不仅在微积分领域至关重要，而且在物理、工程和经济等多个现实应用中也具有重要意义。理解asymptotes（渐近线）可以为我们提供更深刻的见解，帮助我们理解函数及其图形表示的行为。 为了说明asymptotes（渐近线）的概念，可以考虑函数f(x) = 1/x。当x趋向无穷大时，f(x)的值趋近于零，这意味着x轴（y=0）作为一条水平asymptote（渐近线）。同样，当x从右侧趋近于零时，f(x)无限增大，表明在x=0处存在一条垂直asymptote（渐近线）。这些特征展示了asymptotes（渐近线）如何定义一个函数行为的极限。 Asymptotes（渐近线）的重要性超越了纯数学。在物理学中，例如，asymptotes（渐近线）的概念可以在研究抛体运动时观察到。在分析抛体轨迹时，人们可能会注意到，随着抛体的移动，其路径越来越接近某个角度，但实际上永远不会达到。这种想法可以使用asymptotes（渐近线）进行建模，帮助物理学家预测物体的运动行为。 在工程学中，asymptotes（渐近线）在理解材料和结构的极限方面发挥着至关重要的作用。例如，在设计桥梁或建筑物时，工程师必须考虑结构能够承受的最大负载。材料的应力-应变曲线通常会接近一个极限，这可以用asymptote（渐近线）来表示。认识到这些极限确保了建筑项目的安全性和耐久性。 经济学也在各种模型中利用asymptotes（渐近线）这一概念。例如，在收益递减法则中，随着更多资源被加入到生产过程中，额外的产出最终会接近一个最大限度。这种行为可以通过分析asymptotes（渐近线）来进行，从而使经济学家了解何时增加投入不再有利。 此外，具有asymptotes（渐近线）的函数的图形表示可以揭示关键的信息，关于趋势和行为。通过研究这些图形，可以识别关键特征，如截距、转折点和函数的整体形状。这种视觉分析有助于在各个领域做出明智的决策，从金融到环境科学。 总之，asymptotes（渐近线）的概念是数学的一个基本方面，它在多个学科中找到了应用。无论是在微积分、物理、工程还是经济学中，理解asymptotes（渐近线）增强了我们对复杂系统的理解，并帮助我们更好地预测周围世界的行为。通过认识到asymptotes（渐近线）的重要性，我们可以欣赏不同变量之间错综复杂的关系，以及它们对我们理解现实所施加的限制。