1) Lim (4x⁵ -3x+2)/(3+2x³+5x⁵) =Lim (4-3/x⁴+2/x⁵)/(5 +2/x² +3/x⁵) = 4/5.
x→∞ x→∞
--------------
2) Lim (x² -2x)/(x² -4x+4)= Lim x(x -2)/(x -2)² = Lim x/(x -2) → не существует.
x→2 ............................ x→2 ......................x→2
--------------
3) Lim ((√(x-3) -√(x+2) ) *( √(x-3) +√(x+2) )/ (√(x-3) +√(x+2) ) =
x→∞
Lim(-5)/ (√(x-3) +√(x+2) ) =0 .
x→∞
--------------
4) Lim ((7x-3)/(7x+2)) ^(-2x) =Lim ((1-5/(7x+2)) ^( -(7x+2)/5) *(-5/(7x+2)* ( -2x)
x→∞ ..................................... x→∞.................................................................=
=Lim ((1-5/(7x+2)) ^( -(7x+2)/5)) ^ (-5/(7x+2)* ( -2x) =
x→∞ ......................................................................
Lim ((1-5/(7x+2)) ^( -(7x+2)/5)) ^ (10/(7+2/x) =e ^(10/7)
x→∞ ......................................................................