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
Learn how to solve limits by rationalizing problems step by step online.
$\lim_{x\to\infty }\left(\left(x+\sqrt[3]{x^2-x^3+1}\right)\frac{x-\sqrt[3]{x^2-x^3+1}}{x-\sqrt[3]{x^2-x^3+1}}\right)$
Learn how to solve limits by rationalizing problems step by step online. Find the limit of x+(x^2-x^3+1)^(1/3) as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(\sqrt[3]{x^2-x^3+1}\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..
