"Infinitesimals" Example Sentences
1. Infinitesimals are commonly used in calculus.
2. Understanding infinitesimals requires a deep knowledge of mathematics.
3. Newton and Leibniz were the first to introduce infinitesimals into mathematics.
4. We can approximate the value using infinitesimals.
5. Infinitesimals can be used to find derivatives.
6. Infinitesimals are smaller than any nonzero quantity.
7. Different functions have different infinitesimals.
8. Infinitesimals are fundamental in integral calculus.
9. We can calculate the area under a curve using infinitesimals.
10. Infinitesimals are an indispensable tool in real analysis.
11. The concept of infinitesimals can be traced back to ancient Greek mathematicians.
12. Infinitesimals played a key role in the development of calculus.
13. Infinitesimals are often used to solve optimization problems.
14. Infinitesimals are important in the study of limits and continuity.
15. The use of infinitesimals is controversial in mathematics.
16. Both infinitesimals and limits are used in calculus.
17. Infinitesimals are essential in the study of differential equations.
18. Infinitesimals allow us to break complex problems into smaller parts.
19. The concept of infinitesimals was once considered flawed, but it has since been proven to be useful.
20. Infinitesimals form the basis of non-standard analysis.
21. Infinitesimals can be used to calculate volumes of irregular shapes.
22. Infinitesimals have been used to solve problems in physics.
23. We can use infinitesimals to find the maxima and minima of a function.
24. Infinitesimals are used in geometry to measure curved shapes.
25. Infinitesimals are an essential tool in mathematical modeling.
26. Infinitesimals are used to study complex systems with varying speeds.
27. Infinitesimals are a key concept in the field of numerical analysis.
28. We can use infinitesimals to calculate the probability of an event occurring.
29. Infinitesimals are used to study the behavior of populations in biology.
30. Understanding the concept of infinitesimals requires a deep understanding of mathematics.
Common Phases
1. Taking the limit of an infinitesimal quantity;
2. Comparing
infinitesimals of different orders;
3. Expressing a function in terms of infinitesimal changes;
4. Evaluating a derivative using
infinitesimals;
5. Integrating over infinitesimal intervals;
6. Approximating a value using infinitesimal increments;
7. Proving a limit using infinitesimal arguments;
8. Calculating an area using infinitesimal pieces.