$\lim_{x\to\infty }\left(\sqrt[3]{6x^2-x^3}+x\right)$

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$\lim_{x\to\infty }\left(\sqrt[3]{x^2\left(6-x\right)}+x\right)$

Learn how to solve limiti all'infinito problems step by step online. (x)->(infinity)lim((6x^2-x^3)^(1/3)+x). Factor the polynomial 6x^2-x^3 by it's greatest common factor (GCF): x^2. Apply the formula: \left(ab\right)^n=a^nb^n. Simplify \sqrt[3]{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{3}. Apply the formula: \lim_{x\to c}\left(a\right)=\lim_{x\to c}\left(a\frac{conjugate\left(numerator\left(a\right)\right)}{conjugate\left(numerator\left(a\right)\right)}\right), where a=\sqrt[3]{x^{2}}\sqrt[3]{6-x}+x and c=\infty .