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Evaluate the limit $\lim_{x\to\infty }\left(\sqrt{\frac{x+8x^2}{2x^2-1}}\right)$ by replacing all occurrences of $x$ by $\infty $
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$\sqrt{\frac{\infty +8\infty ^2}{2\infty ^2-1}}$
Learn how to solve problems step by step online. Find the limit of ((x+8x^2)/(2x^2-1))^1/2 as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\sqrt{\frac{x+8x^2}{2x^2-1}}\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Any expression multiplied by infinity tends to infinity, in other words: \infty\cdot(\pm n)=\pm\infty, if n\neq0.