Final answer to the problem
$\frac{\sqrt[3]{\left(2\right)^{2}}\sqrt[3]{\left(4\right)^{2}}-4}{\left(\sqrt[3]{2}\sqrt[3]{4}+2\right)\sqrt{3}+\left(-\sqrt[3]{2}\sqrt[3]{4}-2\right)\sqrt{3}}$
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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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1
Factoring by $2$
$\lim_{x\to3}\left(\frac{\sqrt[3]{2\left(1+x\right)}-2}{\sqrt{x}-\sqrt{3}}\right)$
Learn how to solve limits by rationalizing problems step by step online.
$\lim_{x\to3}\left(\frac{\sqrt[3]{2\left(1+x\right)}-2}{\sqrt{x}-\sqrt{3}}\right)$
Learn how to solve limits by rationalizing problems step by step online. Find the limit of ((2x+2)^(1/3)-2)/(x^(1/2)-*3^(1/2)) as x approaches 3. Factoring by 2. The power of a product is equal to the product of it's factors raised to the same power. Applying rationalisation. Multiply and simplify the expression within the limit.
Final answer to the problem
$\frac{\sqrt[3]{\left(2\right)^{2}}\sqrt[3]{\left(4\right)^{2}}-4}{\left(\sqrt[3]{2}\sqrt[3]{4}+2\right)\sqrt{3}+\left(-\sqrt[3]{2}\sqrt[3]{4}-2\right)\sqrt{3}}$
