Второй вариант первое задание<--<br>Y(x) = 2/(3cos(3x - π/6))
ОДЗ: cos(3x - π/6) ≠ 0, 3x - π/6 ≠ π/2 + πk
3x ≠ π/2 + π/6 + πk, 3x ≠ 2π/3 + πk, k∈Z
x ≠ 2π/9 + πk/3, k∈Z
Y = y(a) + y'(a)*(x - a) - уравнение касательной
a = π/3
y(π/3) = 2/(3*cos(3*π/3 - π/6)) = 2/(3*cos(π - π/6)) = -2/(3*cos(π/6)) =-2*2/(3*√3) = -4√3/9
y'(x) = (2/3)*(-1)*(cos^(-2)(3x - π/6))*3 = -2/cos^2(3x - π/6)
y'(π/3) = -2/cos^2(3*π/3 - π/6) = -2/cos^2(π/6) = -2*4/3 = -8/3
Y = -4√3/9 - (8/3)*(x - π/3) = -(8/3)*x - (4√3/9) + (8π/9