Final answer to the problem
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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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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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$\lim_{n\to\infty }\left(\frac{\frac{n^3+n^2-6n^6}{n^8}}{\frac{n^3+n^8+10n^6}{n^8}}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of (n^3+n^2-6n^6)/(n^3+n^810n^6) as n 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 \frac{n^8}{n^8} by n^8. Simplify the fraction by n.
