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Limits of Algebraic functions Questions and solutions as variable approaches infinity

The limits of algebraic functions should be evaluated sometimes when the variable approaches infinity. So, a worksheet that consists of limits of algebraic functions as variable tends to infinity examples is given here for your practice with answers, and also solutions to know how to find the limits of algebraic functions, as the variable approaches infinity questions in various methods by the infinite limits rules.

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \bigg(2+\dfrac{3}{x^2}\bigg)}$

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \dfrac{(x+1)^4-(x-1)^4}{(x+1)^4+(x-1)^4}}$

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

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \dfrac{\sqrt[\Large 3]{x^3+2x-1}}{x+2}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \dfrac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,\infty}{\normalsize \sqrt[\Large 3]{(x+1)^2}-\sqrt[\Large 3]{(x-1)^2}}$

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