# Limits by Rationalization Questions and Solutions

The limits by rationalization is a method of evaluating the limits by rationalizing the irrational form expressions in functions that play a role in giving the indeterminate form. The worksheet on the example limits questions by rationalisation is given for practice and solutions to learn how to find the limits by rationalizing the radical expressions in the functions.

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\sqrt{1+x}-1}{x}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 3}{\normalsize \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize (\sqrt{x^2+2x}-x)}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 4}{\normalsize \dfrac{\sqrt{1+2x}-3}{\sqrt{x}-2}}$

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