1.
(36^5,3)/(6^8,6)=(6^10,6)/(6^8,6)=6^2=36
3.
y=√(2x+15-x²)
2x+15-x²≥0
x²-2x-15≤0
x²-2x-15=0 D=64
x₁=-3 x₂=5 ⇒
(x+3)(x-5)≤0
-∞____+_____-3____-_____5____+_____+∞
x∈[-3;5].
5.
f(x)=x³-3x²+1
f`(x)=3x²-6x>0
3x(x-2)>0
x(x-2)>0
-∞____+_____0_____-_____2_____+_____+∞
x∈(-∞;0)U(2;+∞).