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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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$\lim_{x\to\infty }\left(\frac{\frac{-x^3+6x^2-8x+1}{x^3}}{\frac{3x^2-7x^3+2x-3}{x^3}}\right)$
Learn how to solve problems step by step online. Find the limit of (-x^3+6x^2-8x+1)/(3x^2-7x^32x+-3) 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 . Simplify the fraction by x.