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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$\lim_{h\to0}\left(\frac{\sqrt[4]{x+h}-\sqrt[4]{x}}{\sqrt{x+h}-\sqrt{x}}\frac{\sqrt[4]{x+h}+\sqrt[4]{x}}{\sqrt[4]{x+h}+\sqrt[4]{x}}\right)$
Learn how to solve problems step by step online. Find the limit of ((x+h)^(1/4)-x^(1/4))/((x+h)^(1/2)-x^(1/2)) as h approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify \left(\sqrt[4]{x+h}\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}{4} and n equals 2. Simplify \left(\sqrt[4]{x}\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}{4} and n equals 2.
