Question

Se considera functia f: R \ {-1} ->R, f(x)=$\frac{x^{2} }{x+1}$

Stabiliti daca functia f are limita in x= -1

Answer 1

Răspuns:

Trebuie  calculate limitele laterale in -1

ls= x→ -1 x<-1 lim f(-1)=lim$\frac{(-1)^{2} }{(-1-0+1)} =\frac{+1}{-0}=$-∞

ld= x→ -1 x>-1=lim f(-1)=$limf(-1+0)=\frac{(-1)^{2} }{-1+0+1}=\frac{+1}{+0}$=+∞

ls≠ld => functia  nu are limita   in   x= -1

pas cu pas: