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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 $\lim_{x\to\infty}\left(xe^{\frac{1}{x}}-1\right)$
Find the limit $\lim_{x\to\infty}\left(\sqrt{25x^2+15}-5x\right)$
Find the limit $\lim_{x\to\infty}\left(x-\sqrt{x^2+5}\right)$
Find the limit $\lim_{x\to0}\left(\frac{\left(3a+1\right)}{\left(2x+1\right)^{\frac{1}{x}}}\right)$
Find the limit $\lim_{x\to\infty}2x-\sqrt{x^2+x}$
Find the limit $\lim_{x\to\infty}\left(\left(x^3-8x^2\right)^{\left(\frac{1}{3}\right)}-x\right)$
Find the limit $\lim_{x\to\infty}20x^{\frac{1}{20}}-20$

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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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