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Limits by rationalizing

Definition

Limits that require that we apply rationalization to solve them.

Solved Exercises

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

$\lim_{x\to5}\left(\frac{\sqrt{x-1}-2}{x-5}\right)$

$\lim_{t\to0}\left(\frac{\sqrt{2+t}-\sqrt{2}}{t}\right)$

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

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

$\lim_{x\to-20}\left(\frac{\sqrt{x+31}-\sqrt{11}}{x+20}\right)$

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

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

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

$\lim_{x\to0}\left(\frac{x^2+x}{\sqrt{x+9}-3}\right)$

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