Question

2 примера на предел

Answer 1

5.8.
lim(x→∞) (5x²-4x+2)/(4x²+2x-5).
lim(x→∞) (5-4/x+2/x²)/(4+2/x-5/x²)=(5-0+0)/(4+0-0)=5/4=1¹/₄.
6.8.
lim(x→4) -(2x²-9x+4)/(√(5-x)-√(x-3))
2x²-9x+4=2x²-8x-(x-4)=2x*(x-4)-(x-4)=(x-4)*(2x-1)=2*(x-4)*(x-0,5)
Умножим числитель и знаменатель на (√(5-х)+√(х-3)):
lim(x→4) -(2*(x-4)*(x-0,5)/((√(5-x))²-(√(x-3))²)=
=lim(x→4) -(2*(x-4)*(x-0,5))/(8-2x)=
=lim(x→4) -(2*(x-4)*(x-0,5))*(√(5-x)+√(x-3))/(-2*x-4)=
=lim(x→4) (x-0,5)*(√(5-x)+√(x-3))=(4-0,5)*(√1+√1)=3,5*2=7.