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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$\lim_{x\to0}\left(\frac{\sqrt[3]{x+2}-\sqrt[3]{2}}{\sqrt{x+2}-\sqrt{2}}\frac{\sqrt[3]{x+2}+\sqrt[3]{2}}{\sqrt[3]{x+2}+\sqrt[3]{2}}\right)$
Learn how to solve problems step by step online. Find the limit of ((x+2)^(1/3)-*2^(1/3))/((x+2)^(1/2)-*2^(1/2)) as x approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(\sqrt[3]{x+2}\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. Simplify \left(\sqrt[3]{2}\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.
