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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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$\lim_{w\to\infty }\left(\frac{\frac{3w^2+5w-2}{w^3}}{\frac{5w^3+4w^2+1}{w^3}}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (3w^2+5w+-2)/(5w^3+4w^2+1) as w 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 . Separate the terms of both fractions. Simplify the fraction . Simplify the fraction by w.