Mathegoras

Calculus › Limits of functions › Differences of square roots

Limit of a ratio with roots

High school · ●●●○○ 50 pts

Find lim⁡x→22−2+x213−(4−x)13\lim_{x\rightarrow 2}\frac{2-\sqrt{2+x}}{2^{\frac{1}{3}}-(4-x)^{\frac{1}{3}}} without using L'Hospital's rule. Round your answer to two decimal places.

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limitsrationalising denominatorsdifference of cubesalgebraic limits