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Step-by-step Solution
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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
Learn how to solve differential calculus problems step by step online.
$\lim_{x\to\infty }\left(\left(\sqrt{9x+10}-\sqrt{9x-10}\right)\frac{\sqrt{9x+10}+\sqrt{9x-10}}{\sqrt{9x+10}+\sqrt{9x-10}}\right)\sqrt{x}$
Learn how to solve differential calculus problems step by step online. Find the limit (x)->(infinity)lim((9x+10)^(1/2)-(9x-10)^(1/2))x^(1/2). Applying rationalisation. Multiply and simplify the expression within the limit. Cancel like terms 9x and -9x. Evaluate the limit \lim_{x\to\infty }\left(\frac{20}{\sqrt{9x+10}+\sqrt{9x-10}}\right) by replacing all occurrences of x by \infty .
Final answer to the problem
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