B What Is the Harm in Using Finite dx in Calculus?

AI Thread Summary
Using a finite dx in calculus leads to approximations rather than precise calculations, as it assumes all mass within the interval is concentrated at a single point. This can introduce errors in results, particularly in contexts where accuracy is crucial. The discussion emphasizes that as dx approaches zero, the approximation improves, ultimately leading to the concept of the integral. The harm lies in relying on finite dx for calculations that require exact values, potentially misleading interpretations. Understanding the significance of limits in calculus is essential for accurate mathematical analysis.
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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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