3cos²x - 2,5sin2x - 2sin²x = 0 Разложим sin2x. 3cos²x - 5sinxcosx - 2sin²x = 0 Разделим на cos²x (cosx ≠ 0). 3 - 5tgx - 2tg² = 0 2tg²x + 5tgx - 3 = 0 Пусть t = tgx. 2t² + 5t - 3 = 0 D = 25 + 3•4•2 = 49 = 7². t = (-5 + 7)/4 = 1/2 t = (-5 - 7)/4 = -12/4 = -3 Обратная замена: tgx = 1/2 x = arctg(1/2) + πn, n ∈ Z tgx = -3 x = arctg(-3) + πn, n ∈ Z.
2) √3sinx - cosx = 2
√3/2sinx - 1/2cosx = 1 cos(π/6)sinx - sin(π/6)cosx = 1 По формуле синуса разности аргументов: sin(x - π/6) = 1 x - π/6 = π/2 + 2πn, n ∈ Z x = π/2 + π/6 + 2πn, n ∈ Z x = 2π/3 + 2πn, n ∈ Z.
Limx→∞ 2/(x^2+3x)
Limx→ -1 (3/(x^2+1) - 1/(x+1))
Limx→∞ 3x/(x-2)
Limx→3 (x-3)/(x^2-9)
Limx→∞ (√x2 – 1-x)
Limx→ 1(x^3-1)/(x-1)
Limx→∞ (2x^3+3)/(x^2-4x^3 )
Limx→ 0 4/(3x^2+2x)
Limx→∞ √(〖x^2+5x-x〗^ )
Limx→ -3/2 (4x^2-9)/(x^2+3)
Limx→∞ (x^3+3x^2 )
Limx→ 0 (3x^2+x)/x
Limx→∞ ((4x^3-x^2)/(x^3+3x^2-1))
Limx→ 5 (5-x)/(3-√(〖2x-1〗^( ) ))
Limx→∞ (2x/(x^3+1))
Limx→ 0 (1-√(1-x^2 ))/x^2
Limx→∞ (5x^4-x^3+2x)/x^4
Limx→ 3 (x^2+2x-15)/(x^2-9)
Limx→∞ (3x^2+x+1)/(3x^2+x^2+1)
Хо найдено через lim прибавиться х и limx
Разложим sin2x.
3cos²x - 5sinxcosx - 2sin²x = 0
Разделим на cos²x (cosx ≠ 0).
3 - 5tgx - 2tg² = 0
2tg²x + 5tgx - 3 = 0
Пусть t = tgx.
2t² + 5t - 3 = 0
D = 25 + 3•4•2 = 49 = 7².
t = (-5 + 7)/4 = 1/2
t = (-5 - 7)/4 = -12/4 = -3
Обратная замена:
tgx = 1/2
x = arctg(1/2) + πn, n ∈ Z
tgx = -3
x = arctg(-3) + πn, n ∈ Z.
2) √3sinx - cosx = 2
√3/2sinx - 1/2cosx = 1
cos(π/6)sinx - sin(π/6)cosx = 1
По формуле синуса разности аргументов:
sin(x - π/6) = 1
x - π/6 = π/2 + 2πn, n ∈ Z
x = π/2 + π/6 + 2πn, n ∈ Z
x = 2π/3 + 2πn, n ∈ Z.