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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The limit of the product of a function and a constant is equal to the limit of the function, times the constant: $\displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}$
Learn how to solve limits by rationalizing problems step by step online.
$4\lim_{x\to\infty }\left(x\left(\sqrt{x}-\sqrt{x-1}\right)\right)$
Learn how to solve limits by rationalizing problems step by step online. Find the limit of 4x(x^(1/2)-(x-1)^(1/2)) as x approaches infinity. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Multiply the single term x by each term of the polynomial \left(\sqrt{x}-\sqrt{x-1}\right). When multiplying exponents with same base you can add the exponents: \sqrt{x}x. Applying rationalisation.
