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Limits by rationalizing

Definition

Limits that require that we apply rationalization to solve them.

Solved Exercises

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{n+2}-\sqrt{2}}{n}\right)$

Evaluate $\lim_{x\to 10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{x}\right)$

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{5+x}-1\cdot \sqrt{5}}{x}\right)$

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{1-x}-\sqrt{1+x}}{x}\right)$

Evaluate $\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\right)$

Evaluate $\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

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