- #1
jaredvert
- 61
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dx as change in distance vs dx as infinitesimal x?
Why are they the same notation?Sent from my iPhone using Physics Forums
Why are they the same notation?Sent from my iPhone using Physics Forums
The difference lies in the interpretation of the notation. When dx is used as a change in distance, it represents a finite change in the distance between two points. On the other hand, when dx is used as infinitesimal x, it represents an infinitely small change in the distance.
Both representations have their own advantages and limitations. When dealing with real-world scenarios, dx as change in distance is more accurate as it takes into account the finite nature of distance. However, in mathematical and theoretical applications, dx as infinitesimal x is more accurate as it allows for easier calculations and simplification of equations.
Dx as change in distance and dx as infinitesimal x are related through the concept of limits in calculus. As the change in distance (dx) becomes infinitely small, it approaches the value of infinitesimal x. Therefore, in the limit, the two representations are equivalent.
Sure, let's consider the distance travelled by a car. If we want to calculate the total distance travelled by the car, we would use dx as change in distance. However, if we want to calculate the instantaneous speed of the car at a specific point, we would use dx as infinitesimal x in the velocity equation.
Understanding the difference between these two representations is crucial in accurately interpreting and solving mathematical and scientific problems. It also helps in understanding the concept of limits and how they are used in calculus. Additionally, it allows for a better understanding of the relationship between the real world and mathematical models.