Find the limit of $\sqrt[3]{1-x^3}+x$ as $x$ approaches $\infty $

Find the limit

$\lim_{x\to\infty}\left(\frac{\sqrt{x^2+1}}{x}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{ax^4+bx^2+c}{dx^3+ex^2+fx+g}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{7x^2}{x-x^3}\right)$

Find the limit

$\lim_{x\to3}\frac{x^3-9x}{x^2-3x}$

Find the limit

$\lim_{x\to-3}\left(\frac{x^4-81}{x+3}\right)$

Find the limit

$\lim_{x\to-1}\left(\frac{12x^3+12x^2}{x^4-x^2}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$