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Limits by Rationalizing


Definition

Limits that require that we apply rationalization to solve them.

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Problems Solved

Find the limit $\lim_{x\to6}\left(\frac{6-x\:}{\left(x^2-36\right)\left(2+\sqrt{x-2}\right)}\right)$
Find the limit $\lim_{x\to\infty}\sqrt[3]{\left(x^3+3x^2+2x\right)}-x$
Find the limit $\lim_{x\to\infty}\left(\sqrt{x^6+5x^3}-x^3\right)$
Find the limit $\lim_{x\to\infty}\left(x-\sqrt{x^2-1}\right)$
Find the limit $\lim_{x\to\infty}\left(\sqrt{x^3-x^2}-7x\right)$
Find the limit $\lim_{x\to\infty}\left(\sqrt{4x^2-x+1}-2x\right)$
Find the limit $\lim\:_{x\to\:4}\left(\frac{\sqrt{x^2+2x-8}-4}{x^2-x-12}\right)$

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Related Topics

Limits by L'Hôpital's rule
Operations with Infinity
Limits by Direct Substitution
Limits by Factoring
Limits of Exponential Functions

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