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MathCalculus

Function Limit Calculation When Numerator and Denominator Both Go to Zero

Calculate a function limit when numerator and denominator both go to zero by factoring, and distinguish the indeterminate form from the limit value.

Question

Calculate the function limit

lim⁡x→1x3−x2x−1.\lim_{x\to1}\frac{x^3-x^2}{x-1}.

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Evidence boundary

This page computes the exact expression in CLP-1 Example 1.4.12. The algebra establishes the limit on nearby points where the quotient is defined; it does not assign a value to the original function at x = 1.