Final answer to the problem
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Step-by-step Solution
How should I solve this problem?
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- 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
$\lim_{x\to\infty }\left(\left(\sqrt{x+2}-\sqrt{x}\right)\frac{\sqrt{x+2}+\sqrt{x}}{\sqrt{x+2}+\sqrt{x}}\right)$
Learn how to solve problems step by step online.
$\lim_{x\to\infty }\left(\left(\sqrt{x+2}-\sqrt{x}\right)\frac{\sqrt{x+2}+\sqrt{x}}{\sqrt{x+2}+\sqrt{x}}\right)$
Learn how to solve problems step by step online. Find the limit of (x+2)^(1/2)-x^(1/2) as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Cancel like terms x and -x. Evaluate the limit \lim_{x\to\infty }\left(\frac{2}{\sqrt{x+2}+\sqrt{x}}\right) by replacing all occurrences of x by \infty .
Final answer to the problem
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