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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 $\lim_{x\to-1}\left(\frac{\left(3x^3+5x^2-4x-6\right)}{\sqrt{\left(x+17\right)}-4}\right)$
Find the limit $\lim\:_{x\to\:\infty\:}\left(\sqrt{4x^{2\:}-8x+3}-\sqrt{4x^{2\:}-16x+16}\right)$
Find the limit $\lim_{x\to\infty}\left(\sqrt{x^2+9}-x\right)$
Find the limit $\lim_{x\to\infty}\sqrt{x}\left(\sqrt{x+13}-\sqrt{x+3}\right)$
Find the limit $\lim_{x\to\infty}\left(x+\sqrt[3]{x^2-x^3+1}\right)$
Find the limit $\lim_{x\to-\infty}\left(\frac{\sqrt[3]{6x^2-x^3}+x}{2.1}\right)$
Find the limit $\lim_{x\to0}\frac{\sqrt{1+x^3}-1}{x^3}$

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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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