Learn how to solve problems step by step online. Find the limit of (x^2+2x)^(1/2)-(x^2+x)^(1/2) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\sqrt{x^2+2x}-\sqrt{x^2+x}\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. Applying the property of infinity: \infty+\infty=\infty. Remember that both infinities must have the same sign.

Find the limit of (x^2+2x)^(1/2)-(x^2+x)^(1/2) as x approaches infinity