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- Solve using L'Hôpital's rule
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- 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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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
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$\lim_{x\to{- \infty }}\left(\frac{\frac{\sqrt{5x^2+\sqrt{4-x}}-\sqrt{-5x}}{-x}}{\frac{3+2x}{-x}}\right)$
Learn how to solve problems step by step online. Find the limit of ((5x^2+(4-x)^(1/2))^(1/2)-(-5x)^(1/2))/(3+2x) as x approaches -infinity. 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. Simplify the fraction .
