* * * * * * * * * * * * * * * * * * * * * * *
Решите уравнение f ' (x) =0 f(x) =(x²+1)(x+1)
Объяснение:
f(x)= (x²+1)(x+1) =x³+x²+x+1 ⇒ f ' (x) = 3x²+2x+1
f ' (x) = 0
3x²+2x+1 =0 D=2²-4*3*1 =- 8 < 0 ⇒ квадратное уравнение не имеет
действительныx корней . Имеет комплексных корней :
D₁ =D/4 = (2/2)² - 3*1 = 1² -3 = -2 , √D₁= √-2= i√2, где i= √-1 i²= -1
x₁ = (-1 - i√2)/3 , x₂ = (-1+ i√2)/3
* * * (U*V) ' = U'V +V'*U и (U+V) ' = U' + V ' (xⁿ) ' =n*xⁿ ⁻¹ * * *
f'(x) =( (x²+1)(x+1) ) ' = 3x²+2x+1
действительно:
f'(x) = (x²+1)' (x+1) + (x+1)' (x²+1) =( (x²)' +1')(x+1)+(x'+1')*( x²+1) = (2x+0)(x+1) +(1+0)(x²+1 )= 2x(x+1) +x²+1 = 2x²+2x +x²+1 =3x²+2x+1 .
3x²+2x+1 =0 ⇔ x²+(2/3)x+1/3 =0 x₁ +x₂ = -2/3 x₁ * x₂ =1/3
* * * * * * * * * * * * * * * * * * * * * *
21sin(x) + 20cos(x) = 14,5
ответ: - arcsin(20/29) + (-1)ⁿ (π/6) +π*n , n ∈ ℤ .
Объяснение: метод вс угла
* * *asinα+bcosα =√(a²+b²)sin(x +φ) , где φ =arctg(b/a) * * *
21sin(x) + 20cos(x) = 14,5 ; √(21²+20²) =√( 441+400 =√881 =29
29( (21/29)*sin(x) + (20/29)*cos(x) )= 29/2 ;
(21/29)*sin(x) + (20/29)*cos(x) =1/2 * * * (21/29)²+(20/29)² =1 * *
обоз. 21/29 =cosφ ⇒ 20/29 = sinφ φ =arcsin(20/29)
sin(x +φ) = 1/2 ;
x +φ = (-1)ⁿ (π/6) +π*n , n ∈ ℤ
x = - φ + (-1)ⁿ (π/6) +π*n , n ∈ ℤ
x = - arcsin(20/29) + (-1)ⁿ (π/6) +π*n , n ∈ ℤ .
очевидно ,что можно и обозначить
21/29 =sinφ ⇒ 20/29 = cosφ φ =arccos(20/29) * * *
cos(x - φ) = 1/2 ⇒ x - φ =±π/3 +2πn , n ∈ ℤ⇔ x = φ ±π/3 +2πn , n ∈ ℤ ;
x = arccos(20/29) ± π/3 +2πn , n ∈ ℤ .
9: 43
<
Social Studies
5 points
Question from Egor9klass
Why civil
society in developed countries
formed only in
the last two centuries?
Answer
VERIFIED RESPONSE
Account deleted •
Civil
society is possible only under legal conditions
(democratic)
states. That's why it
formed in developed countries only in
the last two centuries, since before
this was the case in an authoritarian and totalitarian way
mode in which
civil society is functioning normally
can't.
4.0 (64)
COMMENT
estimate
thanks
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