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We could not solve this problem by using the method: Limits by Factoring
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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$\lim_{x\to\infty }\left(\frac{\frac{x^3+1}{x^3}}{\frac{3x^3-1}{x^3}}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (x^3+1)/(3x^3-1) 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 . Separate the terms of both fractions. Simplify the fraction \frac{3x^3}{x^3} by x^3. Simplify the fraction \frac{x^3}{x^3} by x^3.