АХ
Александр Холодилин
1) а)4sin(x) = 3
sin(x) = ±√3/2
x = π/3 + πk, k - целое.
б) sin(2x + π/3) + cos(2x + π/3) = 0
√2cos(2x + π/12) = 0
2x + π/12 = π/2 + πk
x = 5π/24 + πk/2, k - целое.
2) f'(x) = (x + 2x - 2(x+1)sin(x) - 1)/(x+1)
f'(0) = -1
Ответ: -1
3) а) 2cos(x) ≤ -√2
cos(x) ≤ -√2/2
3π/4 + 2πk ≤ x ≤ 5π/4 + 2πk, k - целое.
б) (x(x-1))/(x-3) > 0
Методом интервалов: