1. y=log₂(2x+3)
2.y=1/3cos(3x-π/2)-π³-e², x₀=π/3
y'=1/3 (-sin(3x-π/2))*3=-sin(3x-π/2)
y'(x₀)=-sin(3*π/3-π/2)=-sin(π-π/2)=-sin(π/2)=-1
3. y=x², x₀=0,25
y'=2x
k=y'(x₀)=2*0,25=0,5
4. sin(π/6-3x)-1/2=0
sin(π/6-3x)=1/2
π/6-3x=π/2+2πn
3x=π/6-π/2+2πn=π/6-3π/6+2πn=-2π/6+2πn=-π/3+2πn
x=-π/9+2πn/3 , n∈Z
1)36a12b7/54a8b11=6•3•7/9•2•11=6•21/18•11=21/3•11=21/33=7/11
2)18mn-27n/9mn=9n(2m-3)/9mn=2m-3/m
3)3c-15/c^2-25=3(c-5)/(c-5)(c+5)=3/c+5
<span>3(5-x)-(5-x)+13=4-(3x-8)
15-3x-5+x+13=4-3x-32
10-2x+13=</span>4-3x-32
-2x+23=-3x-28
-2x+3x=-28-23
x=-51
Ответ: корень уравнения равен -51.