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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When multiplying exponents with same base you can add the exponents: $-x\sqrt{x}$
Learn how to solve limits by rationalizing problems step by step online.
$\lim_{x\to\infty }\left(\frac{x\sqrt{x+2}-\sqrt{x^{3}}}{x}\right)$
Learn how to solve limits by rationalizing problems step by step online. Find the limit of (x(x+2)^(1/2)-xx^(1/2))/x as x approaches infinity. When multiplying exponents with same base you can add the exponents: -x\sqrt{x}. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical. Separate the terms of both fractions.
