Question

помогите решить 1-5 примеры очень надо

Answer 1

1) lim(x→5) (x²-25)/(x-5)=lim(x→5) (x-5)(x+5)/(x-5)=lim(x→5) (x+5)=10.
2) lim(x→-0,5) (6x²-x-1)/(x-0,5)=lim(x→-0,5) (x-0,5)(x+1/3)/(x-0,5)=
=lim(x→-0,5) (x+1/3)=-1/2+1/3=-1/6.
3) lim(x→5) (5-x)/(3-√(2x-1))=lim(x→5)=
=(5-x)(3+√(2x-1))/(3-√(2x-1))(3+√(2x-1))=
lim(x→5) (5-x)(3+√(2x-1)/(9-2x+1)=lim(x→5)(5-x)(3+√(2x-1))/(10-2x)=
=lim(x→5) (5-x)(3+√(2x-1))/(2*(5-x))=lim(x→5) (3+√(2x-1)/2=
=(3+√(2*5-1))/2=(3+√9)/2=3.
4) lim(x→∞) (1-x⁴)/(-6x⁴-2x²+1)
Разделим числитель и знаменатель на x⁴:
lim(x→∞) (1/x⁴-1)/(-6x⁴/x⁴-2x²/x⁴+1/x⁴)=-1/(-6)=1/6.
5) lim(x→∞) (2x-5)/5=lim(x→∞) (0,2x-1)=∞.