f'(x)=(2x³)'-(9x²)'+(12x)'+1'=6x²-18x+12
[tex] \lim_{x \to \infty} \frac{2x^3-2x^3+9 x^{2} -12x-1}{6 x^{2} -18x+12}= \lim_{n \to \infty} \frac{9x^2-12x-1}{6 x^{2} -18x+12}= \\ = \lim_{n \to \infty} \frac{x^2(9- \frac{12}{x}- \frac{1}{ x^{2} }) }{ x^{2} (6- \frac{18}{x}+ \frac{12}{ x^{2} } ) }= \frac{9}{6}= \frac{3}{2} [/tex]
