Find the limit of $\frac{1-x\left(x^3-6x^2\right)^{-\frac{1}{3}}}{\left(x^3-6x^2\right)^{-\frac{1}{3}}}$ as $x$ approaches $\infty $

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Learn how to solve limits by factoring problems step by step online. Find the limit of (1-x(x^3-6x^2)^(-1/3))/((x^3-6x^2)^(-1/3)) as x approaches infinity. Factor the polynomial \left(x^3-6x^2\right) by it's greatest common factor (GCF): x^2. Factor the polynomial \left(x^3-6x^2\right) by it's greatest common factor (GCF): x^2. Evaluate the limit \lim_{x\to\infty }\left(\frac{1-x\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}{\left(x^2\left(x-6\right)\right)^{-\frac{1}{3}}}\right) by replacing all occurrences of x by \infty . Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty.