Find the limit of $\arctan\left(\frac{x^2+\sqrt{x}}{\sqrt[3]{x}-\sqrt{3x^2}}\right)$ as $x$ approaches $\infty $

Learn how to solve operations with infinity problems step by step online. Find the limit of arctan((x^2+x^(1/2))/(x^(1/3)-(3x^2)^(1/2))) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\arctan\left(\frac{x^2+\sqrt{x}}{\sqrt[3]{x}-\sqrt{3x^2}}\right)\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \sqrt{\infty }=\infty. Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty. Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty.