Final answer to the problem
Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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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 $
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$\arctan\left(\frac{\infty ^2+\sqrt{\infty }}{\sqrt[3]{\infty }-\sqrt{3\cdot \infty ^2}}\right)$
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.
