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
ОДЗ x²-x-2≥0
x1+x2=1 U x1*x2=-2
x1=-1 U x2=2
+ _ +
--------[-1]------------[2]---------
x≤-1 U x≥2
√(x²-x-2)≥0⇒(x-4)/(x-5)≤0
x=4 x=5
//////////////////////////
+ _ +
----[-1]----[4]----------[2]----(5)-----------
//////// \\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈[2;5)
( а + b )^2 + ( a - b )^2 < = 3( a^2 + b^2 )
a^2 + 2ab + b^2 + a^2 - 2ab + b^2 <= 3( a^2 + b^2 )
2a^2 + 2b^2 < = 3( a^2 + b^2 )
2( a^2 + b^2 ) < = 3( a^2 + b^2 )
2 < 3
1) 5 ^ - 4/5 * 5 ^ 1/5 = 5 ^ - 3/5
2) ( 5 ^ - 3/5 ) ^ 5 = 5 ^ - 3
3) ( 5 ^ - 5 ) : ( 5 ^ - 3 ) = 5 ^ - 2 = 1/25 = 0,04
Ответ 0,04
5x-12x-42=13-x-1
5x-12x+x=13-1+42
-6x=54
X=-9