Question

Lim где Х стремится к 3 x^2-5x+6/x^2-9

Answer 1

lim(x-->3)[(x²-5x+6)/(x²-9)]=0/0;
lim(x-->3)[(x²-6x+9+x-3)]/[(x+3)·(x-3)]=
=lim(x-->3)[(x-3)²+(x-3)]/(x+3)(x-3)=lim(x-->3)[(x-3)(x-3+1)/(x+3)(x-3)=
=lim(x-->3)[(x-2)/(x+3)]=(3-2)/(3+3)=1/6;