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
X*2+4x-21=0
x1=-7
x2=3
x*2+4x-21=(x+7)(x-3)
домножим ур-е на (х+7)(х-3), получим
(5x-1)(x-3)-2x+2(x+7)+63=0
5x*2-15x-x+3-2x+2x+14+63=0
5x*2-16x+80=0
D<0
корней нет
<span> у=х^ tgx
lny=ln(</span>х^ tgx)
<span>
(1/y)y'=(tgx</span>·lnx)' y'=y·[(1/cos²x)·lnx+(tgx)/x] =(х^ tgx)[(lnx/cos²x)+(tgx)/x] <span>
</span>