3. 4*0,5^(x(x+3)) < 0.25^(2x)
2² * (2⁻¹)^(x²+3x) < (2⁻²)^(2x)
2^(2-x²-3x)<2^(-4x)<br>2-x²-3x<-4x<br>-x²-3x+4x+2<0<br>-x²+x+2<0<br>x²-x-2>0
x²-x-2=0
D=1+8=9
x₁=1-3= -1
2
x₂=1+3=2
2
+ - +
-------- -1 ---------- 2 ----------------
\\\\\\\\\ \\\\\\\\\\\\\\\\
x∈(-∞; -1)U(2; +∞)
4. f(x)=x sin(2x-3)
f(x)' = x' sin(2x-3) + x (sin(2x-3))' = sin(2x-3) + 2x cos(2x-3)