![\displaystyle\lim_{x\to+\infty}\left( \sqrt[3]{x^3+x^2+x+1}-\sqrt{x^2+x+1}\cdot\frac{\ln(e^x+x)}{x} \right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%28+%5Csqrt%5B3%5D%7Bx%5E3%2Bx%5E2%2Bx%2B1%7D-%5Csqrt%7Bx%5E2%2Bx%2B1%7D%5Ccdot%5Cfrac%7B%5Cln%28e%5Ex%2Bx%29%7D%7Bx%7D+%5Cright%29 "\displaystyle\lim_{x\to+\infty}\left( \sqrt[3]{x^3+x^2+x+1}-\sqrt{x^2+x+1}\cdot\frac{\ln(e^x+x)}{x} \right)")
NOTE :
As per L'Hôpital's rule, Mean value theorem, Taylor's theorem but still don't have this skill.
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