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The limit of a polynomial function ($\sqrt{x^2+3x}-x$) 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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$\lim_{x\to\infty }\left(\sqrt{x^2+3x}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2+3x)^1/2-x as x approaches infinity. The limit of a polynomial function (\sqrt{x^2+3x}-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. Evaluate the limit \lim_{x\to\infty }\left(\sqrt{x^2+3x}\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. Any expression multiplied by infinity tends to infinity, in other words: \infty\cdot(\pm n)=\pm\infty, if n\neq0.