Răspuns
f(x)={[x²+2x]/(x-1) x≥0
{(x²-2x)/(x-1) x<0
Ecuatia asimptotei
y=mx+n
m=x→∞=lim f(x)/x=lim(x²+2x)/x(x-1)=lim(x²+2x)/(x²-1)=1
n=x→+∞ lim(f(x)-mx)=lim (x²+2x)/(x-1)-x)=lim(x²+2x-x(x-1))/(x-1)=lim[x²+2x-x²+x]/(x-1)=
lim(3x/((x-1)=3
y=x+3 asimptota oblica spre +∞
__________________________________________________
Asimptota spre -∞
m= x→-∞ lim[(x²-2x)/x(x-1)]=lim(x²-2x)/(x²-x)=1
x→-∞
n=lim(x²-2x)/(x-1)-x)=lim(x²-2x-x(x-1))=lim(x²-2x-x²+x)/(x-1)=
lim(-x)/(x-1)= -1
y=x-1 asiptota la -∞
Explicație pas cu pas:
