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Evaluate the limit $\lim_{x\to\infty }\left(\sqrt{x^2-5x+6}-x\right)$ by replacing all occurrences of $x$ by $\infty $
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$\sqrt{\infty ^2-5\cdot \infty +6}- \infty $
Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2-5x+6)^1/2-x as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\sqrt{x^2-5x+6}-x\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so =\infty. Any expression multiplied by infinity tends to infinity, in other words: \infty\cdot(\pm n)=\pm\infty, if n\neq0. Infinity minus infinity is an indeterminate form.