100 Examples of sentences containing the adjective "asymptotic"

Definition

As an adjective, asymptotic refers to a behavior or property of a function or sequence that approaches a limit or value as an argument or variable tends toward infinity or some specified point. It is often used in mathematics and statistics to describe the characteristics of estimators or functions in the context of their limiting behavior.

Synonyms

• Limitless
• Approaching
• Converging
• Near
• Tending

Antonyms

• Divergent
• Unbounded
• Non-converging
• Far
• Distant

Examples

1. The asymptotic behavior of the function can be analyzed to determine its long-term trends.
2. In statistics, the asymptotic distribution of an estimator is important for hypothesis testing.
3. We studied the asymptotic properties of the algorithm to ensure its efficiency.
4. The graph shows the asymptotic approach to the x-axis as x increases.
5. The asymptotic analysis revealed that the time complexity was logarithmic.
6. As n approaches infinity, the series exhibits asymptotic growth.
7. The asymptotic nature of the solution allows us to approximate its behavior for large values.
8. Understanding the asymptotic limits is crucial for modeling real-world phenomena.
9. The asymptotic formula provides a clearer picture of the function's behavior.
10. Researchers employed asymptotic methods to solve the differential equations.
11. The concept of asymptotic stability is key in control theory.
12. An asymptotic analysis can simplify complex problems significantly.
13. The asymptotic expansion helps in approximating the integral.
14. As we derived the equation, the asymptotic terms became evident.
15. The asymptotic nature of the curve indicates a limit to its growth.
16. We focused on the asymptotic characteristics to derive conclusions.
17. The asymptotic behavior of the sequence led to interesting results in number theory.
18. In the study of algorithms, asymptotic notation is commonly used.
19. The asymptotic analysis showed that the function stabilizes after a certain point.
20. The researcher highlighted the asymptotic efficiency of the proposed method.
21. As the sample size increases, the asymptotic normality of the estimator becomes apparent.
22. The asymptotic theory underpins many statistical models.
23. In physics, the asymptotic behavior of particles is significant at high energies.
24. The article discussed the asymptotic limits of the proposed model.
25. The asymptotic properties were derived using advanced calculus techniques.
26. The asymptotic analysis provided insights into the convergence of the series.
27. The asymptotic relationship between the variables was significant in the study.
28. The findings demonstrated the asymptotic stability of the system.
29. Asymptotic analysis is used extensively in computer science.
30. The asymptotic nature of the model helped predict future trends.
31. The paper elaborated on the asymptotic behavior of the population dynamics.
32. The asymptotic results were consistent with previous studies.
33. In calculus, we often explore the asymptotic behavior of functions.
34. The asymptotic curve indicated a clear trend toward a limit.
35. We found the asymptotic method to be quite effective in our calculations.
36. The asymptotic properties of the function were essential for our analysis.
37. The asymptotic behavior of the integrals was a key focus of the research.
38. Understanding asymptotic behavior can lead to improved algorithms.
39. The asymptotic expansion provided a better approximation for small values.
40. The asymptotic limits of the process were thoroughly investigated.
41. The team's findings on asymptotic efficiency were groundbreaking.
42. The asymptotic nature of the results was unexpected.
43. Many mathematical models rely on asymptotic approximations.
44. The asymptotic stability of the equilibrium point was proven mathematically.
45. We derived the asymptotic form of the solution through rigorous analysis.
46. The asymptotic behavior of the function is crucial for long-term predictions.
47. The results displayed asymptotic characteristics that matched theoretical predictions.
48. The asymptotic convergence of the series was confirmed by simulations.
49. The paper focused on asymptotic behaviors in large-scale systems.
50. The asymptotic approach allowed us to simplify the problem significantly.
51. The algorithm's asymptotic performance was compared to existing methods.
52. The asymptotic behavior of the process was thoroughly modeled.
53. In fluid dynamics, asymptotic analysis can simplify complex equations.
54. The study examined the asymptotic limits of the proposed model.
55. The concept of asymptotic efficiency is vital in statistical estimation.
56. The asymptotic properties influenced our understanding of the data.
57. We were interested in the asymptotic behavior of the solutions.
58. The asymptotic properties of the integrals were analyzed in detail.
59. As the data set increased, we noted asymptotic behavior in the results.
60. The asymptotic analysis revealed potential issues with the model.
61. The research highlighted the asymptotic nature of the findings.
62. The asymptotic characteristics were essential for the theory's development.
63. The asymptotic stability of the system was a key finding.
64. The asymptotic relationships helped clarify the model's predictions.
65. The study provided insights into the asymptotic behavior of the estimates.
66. The asymptotic analysis confirmed previous theoretical results.
67. The asymptotic approach was crucial for simplifying the calculations.
68. Understanding the asymptotic behavior of the function is essential in optimization.
69. The findings were consistent with asymptotic predictions.
70. The asymptotic convergence of the series was visually evident.
71. The results demonstrated clear asymptotic behavior.
72. The asymptotic limits were analyzed to predict future trends.
73. In machine learning, asymptotic properties can influence model selection.
74. The asymptotic nature of the function was a focal point of the research.
75. The asymptotic analysis provided clarity on the system's behavior.
76. The team utilized an asymptotic approach to simplify the problem.
77. The asymptotic behavior of the model showed significant improvements.
78. The study analyzed the asymptotic characteristics of the data.
79. The asymptotic properties were derived from first principles.
80. We investigated the asymptotic behavior of various algorithms.
81. The asymptotic approach yielded promising results.
82. The findings suggested asymptotic stability in the proposed solutions.
83. The asymptotic analysis served as a foundation for further research.
84. The asymptotic curve provided valuable insights into the system.
85. The results demonstrated an asymptotic relationship between the variables.
86. The asymptotic behavior of the system was consistent with theoretical expectations.
87. The team focused on the asymptotic properties of the function.
88. We derived the asymptotic limits using numerical methods.
89. The asymptotic characteristics were a key part of the analysis.
90. The asymptotic analysis allowed for better understanding of the data trends.
91. The asymptotic nature of the predictions was noteworthy.
92. We discovered interesting asymptotic properties in our study.
93. The asymptotic approach simplified the complex calculations.
94. The analysis focused on the asymptotic behavior of the model.
95. The asymptotic behavior of the function was critical for predictions.
96. The findings were consistent with asymptotic theoretical frameworks.
97. The asymptotic analysis revealed underlying structures in the data.
98. The paper discussed the asymptotic nature of convergence in detail.
99. The asymptotic properties provided insights into long-term behavior.
100. Understanding asymptotic behavior is essential for advanced mathematical modeling.