Find the limit of $\frac{x+x^2}{1-2x^2}$ 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

$\lim_{x\to\infty}\left(\frac{e^x}{x^2}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{ln\left(x\right)}{\sqrt{x}}\right)$

Find the limit

$\lim_{x\to\infty}\left(\frac{\ln\left(x\right)}{x^2}\right)$

Find the limit

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

Find the limit

$\lim_{x\to\infty}\left(xe^{-x}\right)$