Mathegoras

Calculus › Limits of functions › Differences of square roots

Limit of quotient of root differences

High school · ●●○○○ 20 pts

Find lim⁡x→0(1+x)1/2−1(1+x)1/3−1\lim_{x \to 0} \frac{(1+x)^{1/2} -1}{(1+x)^{1/3} -1} without using L'Hôpital's rule. Round to three decimal places.

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limitsrationalising denominatorslimit laws