Se considera functia f: (-inf,-2]U[0, +inf)
f(x)=x+sqrt(x^2 +2x)
Sa se determine asimptotele orizontale sau oblice.
Asimptota
asimtote orizintale
lim(x->-inf)f(x)=lim(x_>-INF)(X^2-|X^2+2x|)/(x-sqrt(x^2+2x))->-1=y-asimptota orizontala spre -inf.si nu are asimptota oblicaSpre +inf. are asimptota oblica y=mx+n unde m=lim(x-.>+inf)f(x)/x=2si n=lim(x->+inf)(f(x)-mx)=sqrt(x^2+2x)-x=2x/(sqrt(x^2+2x)+x)=1dci a.o.este y=2x+1 spre +inf.si nu are a orizintala
lim(x->-inf)f(x)=lim(x_>-INF)(X^2-|X^2+2x|)/(x-sqrt(x^2+2x))->-1=y-asimptota orizontala spre -inf.si nu are asimptota oblicaSpre +inf. are asimptota oblica y=mx+n unde m=lim(x-.>+inf)f(x)/x=2si n=lim(x->+inf)(f(x)-mx)=sqrt(x^2+2x)-x=2x/(sqrt(x^2+2x)+x)=1dci a.o.este y=2x+1 spre +inf.si nu are a orizintala