Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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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Applying rationalisation
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$\lim_{x\to\infty }\left(\left(\sqrt[3]{x^3+3x^2+2x}-x\right)\frac{\sqrt[3]{x^3+3x^2+2x}+x}{\sqrt[3]{x^3+3x^2+2x}+x}\right)$
Learn how to solve problems step by step online. Find the limit of (x^3+3x^22x)^(1/3)-x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(\sqrt[3]{x^3+3x^2+2x}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{3} and n equals 2. The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: \displaystyle\frac{a^2-b^2}{a+b}=a-b..
