Find the following limits :

$\underset{x}{lim}\frac{3x^2-4x^6-2}{x^2+12x^6+4}$

$\underset{x-}{lim}\frac{5x-4x^3}{12x^4+1}$

$\underset{x-}{lim}\frac{8x^5-4x-1}{12x^3+4}$

$2$

$\underset{x}{lim}ta{n}^{-1}x$

$\underset{x}{lim}co{s}^{-1}(\frac{1}{x})$

$(6)\underset{x}{lim}{e}^{-\frac{1}{x^2}}$

Find the horizontal and vertical asymptote lines of the graph of the functions:

$f(x)=\frac{x+3}{2x-9}$

$f(x)=\sqrt[\phantom{2}]{x^2+1}-x$

$f(x)=ta{n}^{-1}x$

$f(x)=e^{-x}$

$f(x)=ln(x-22)$