Question

Putin ajutor va rog
1. f:R→R
f(x)= 2x^{3} -9 x^{2} +12x+1

b)$\lim_{x \to \infty} \frac{2 x^{3}-f(x) }{f'(x)}$

Answer 1

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