Redefining 'e' with Pre-Calculus: An Intuitive Approach
2025-04-17
This article elegantly redefines the natural logarithm base 'e' using pre-calculus, rather than calculus. It leverages geometric intuition, explaining that all exponential curves (with positive real bases) are horizontal stretches of a single curve. By calculating the slope of the tangent line at x=0, it approximates 'e' and further proves that the tangent slope of eˣ is always equal to its y-value, mirroring the derivative concept in calculus. Finally, it visually demonstrates the equivalence of this definition with the compound interest limit, providing a more intuitive and accessible understanding of 'e'.
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Misc
pre-calculus