Mathegoras

Calculus › Limits of functions › Differences of square roots

Parameters of a square-root limit

High school · ●●●○○ 50 pts

Find the values of the constants aa and bb such that lim⁡x→1a−x−b+xx−1=−12\lim_{x \to 1} \frac{\sqrt{a-x} - \sqrt{b+x}}{x-1} = -\frac{1}{2}.

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limitsrationalising the numerator