What Is the Harm in Using Finite dx in Calculus?

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SUMMARY

The discussion centers on the implications of using a finite differential element, denoted as dx, in calculus. It highlights that employing a finite dx results in an approximation of the mass element between x and x + dx, which assumes all mass is concentrated at position x. As dx approaches zero, the approximation improves, leading to the formal definition of the integral. This distinction is crucial for understanding the transition from discrete to continuous mathematics.

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  • Familiarity with differential notation and its applications.
  • Knowledge of approximation methods in mathematical analysis.
  • Basic grasp of the concept of mass elements in physics.
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  • Study the formal definition of integrals in calculus.
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  • Learn about approximation techniques in mathematical analysis.
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navneet9431
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What does the author want to say through these lines?
What is the *harm* he is talking about?

I will be thankful for any help!
 

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It's a strange way to describe things. The calculation involving a finite ##dx## is an approximation. You effectively take the mass element from ##x## to ##x + dx## all to be at position ##x##. As ##dx## gets smaller, the approximation gets better. The limit ##dx \rightarrow 0## is the integral.
 

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