Ln as Limit of Root and Reciprocal Functions
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This example demonstrates how the logarithmic function ln(x) can be approximated by the limit of root and reciprocal functions. Key math concepts include limits, root functions, reciprocal functions, and the continuity of logarithmic functions. GeoGebra commands used are f (function object), rootpower (root function), root (square root), reciprocalpower (reciprocal function), and reciprocal (reciprocal). Suitable for high school and above students to understand the limit properties of logarithmic functions and function approximation concepts.
GeoGebra Commands & Parameters
f(x) = log(x)Numeric rootpower(0.09)root(x) = (rootpower^(-1) * (x^(rootpower) - 1))Numeric reciprocalpower(-0.1)reciprocal(x) = (reciprocalpower^(-1) * (x^(reciprocalpower) - 1))