<s>[INST] Determine the limiting behaviour of $\lim_{x \to \infty}{\frac{\sqrt{x^4+1}}{\sqrt[3]{x^6+1}}}$ Determine the limiting behaviour of $\lim_{x \to \infty}{\dfrac{\sqrt{x^4+1}}{\sqrt[3]{x^6+1}}}$
Used L'Hopitals to get $\;\dfrac{(x^6+1)^{\frac{2}{3}}}{x^2 \sqrt{x^4+1}}$ but not sure what more i can do after that.
 [/INST] HINT
$$\dfrac{\sqrt{x^4+1}}{\sqrt[3]{x^6+1}} = \dfrac{x^2 \sqrt{1+1/x^4}}{x^2 \sqrt[3]{1+1/x^6}} = \dfrac{\sqrt{1+1/x^4}}{\sqrt[3]{1+1/x^6}}$$
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