asymptotically

asymptotically的音标为[ˌæsɪmptəˈtɪsli]，基本翻译为“近似的；渐进地”，速记技巧为“as（as…）+ sym（相同）+ pt（部分）+ otot（看作单词total，全部的）+ ly（副词词尾）= 近似地”。

英文单词“asymptotically”来源于希腊语词根“asymptotes”，意为“无限接近但不相交”。其变化形式主要有“asymptote”、“asymptotically”和“asymptotic”。

相关单词：

1. “asymptote”意为“渐近线”，表示两条曲线无限接近但不相交的情形。例如，y=2x是一条曲线，而y=x+2是一条渐近线，它们在无限远处接近但不相交。

2. “asymptotically equal”意为“在某种意义上相等”，常用于数学和物理中描述两个量在无限接近时的关系。

3. “asymptotic”意为“近似的”，表示接近但不完全等同。这个词也用于描述物理中的渐近行为，如等时曲线的渐近线。

例如，在描述粒子在强相互作用下的行为时，科学家们使用了“asymptotic freedom”一词，意为这种相互作用在接近临界点时变得“自由”或“稀疏”，这有助于理解这种现象在更高层次上的行为。

总之，“asymptotically”这个词描述了无限接近但不完全相交的情况，常用于数学、物理和工程学中。

常用短语：

1. asymptotically approach

2. asymptotically equal

3. asymptotically increasing

4. asymptotically linear

5. asymptotically stable

6. asymptotic velocity

7. asymptotically zero

双语例句：

1. The function asymptotically approaches the limit as x approaches infinity.

随着x接近无穷大，该函数渐近地接近极限。

2. The number of students enrolling in the course is asymptotically equal to the number of seats available.

报名该课程的学生人数与可用座位数渐近相等。

3. The company"s profits are asymptotically increasing as it expands its operations.

随着公司业务的扩大，其利润渐近地增加。

4. The stock market"s price is asymptotically linear with time.

股票市场的价格与时间呈渐近线型关系。

5. The system is asymptotically stable if the eigenvalues have negative real parts.

如果系统的特征值有负实部，则系统是渐近稳定的。

6. The velocity of the object asymptotically approaches zero as it falls towards the ground.

物体在向地面下落时，其速度渐近地接近零。

7. The number of visitors to the website is asymptotically zero as time passes by.

随着时间的推移，网站访问量渐近地减少为零。

英文小作文：

Asymptotic Growth

In science, asymptotic growth refers to a situation where a quantity grows at a constant rate without bound, approaching a certain limit as time passes. This concept can be applied to many real-life situations, such as the growth of a population, the expansion of a company, or the velocity of an object falling towards the ground.

For example, consider a company that is constantly expanding its operations and hiring new employees. Over time, the company"s revenue and profits will grow at a constant rate, approaching infinity as it becomes more successful and profitable. Similarly, consider a population that is constantly increasing in size, with each new birth contributing to the overall growth of the population. As time passes, the size of the population will continue to grow, approaching infinity asymptotically.

In this context, asymptotic growth refers to a situation where a quantity keeps growing at a constant rate without bound, approaching a certain limit as time passes. It emphasizes the importance of continuous effort and sustained growth, rather than relying solely on initial conditions or luck to achieve success. Therefore, it is essential to maintain a growth mindset and stay focused on continuous improvement and innovation to achieve asymptotic growth in any field.