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The limit of a polynomial function ($\sqrt{x^2-5x+6}-x$) when $x$ tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term

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$\lim_{x\to\infty }\left(-x\right)$

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 \infty. The limit of a polynomial function (\sqrt{x^2-5x+6}-x) when x tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Evaluate the limit \lim_{x\to\infty }\left(x\right) by replacing all occurrences of x by \infty .