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Limits by rationalizing

Definition

Limits that require that we apply rationalization to solve them.

Solved Exercises

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

Evaluate the limit $\lim_{x\to0}\left(\frac{\sqrt{5x+4}-2}{x}\right)$

Evaluate the limit $\lim_{x\to 3}\left(\frac{\sqrt{2x+3}-x}{x-3}\right)$

Evaluate the limit $\lim_{x\to a}\left(\frac{\sqrt{b^2-x}-\sqrt{b^2-a}}{x-a}\right)$

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

Evaluate the limit $\lim_{x\to2}\left(\frac{3-\sqrt{5x-1}}{x-2}\right)$

Evaluate the limit $\lim_{w\to0}\left(\frac{\sqrt{w}}{\sqrt{w+3}-\sqrt{3}}\right)$

Evaluate the limit $\lim_{x\to0}\left(\frac{\sqrt{x^2+1}-1}{x^2}\right)$

Evaluate the limit $\lim_{x\to-2}\left(\frac{3-\sqrt{6x+21}}{x+2}\right)$

Evaluate the limit $\lim_{x\to3}\left(\frac{x-3}{2-\sqrt{x+1}}\right)$

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