Сумма п членов геометрической прогрессии находится по формуле
S = x1(1 - q^n)/(1 - q)
Подставим S = 210 , q = 2 и n = 4
210 = x1 ·(1 - 2^4)/( 1 - 2)
210 = x1 · 15
x1 = 210 : 15
x1 = 14
x2 = 14·2 = 28
x3 = 28 · 2 = 56
x4 = 56 · 2 = 112
1) m^4 - n^4 = ( m^2 )^2 - ( n^2 )^2 = ( m^2 - n^2 )( m^2 + n^2 )
2) m^2 - n^2 - ( m^2 - n^2 )( m^2 + n^2 ) = ( m^2 - n^2 )( 1 - ( m^2 + n^2 )) = ( m^2 - n^2 )( 1 - m^2 - n^2 )
-4х-8+3х-3-2=4х-8+9
-4х-4х+3х=9+5
-5х=14
х=-14/5
Possible derivation:
d/dx(y) = d/dx(1/2 cos(2 x)-x)
The derivative of y is zero:
0 = d/dx(-x+1/2 cos(2 x))
Differentiate the sum term by term and factor out constants:
0 = (d/dx(cos(2 x)))/2-d/dx(x)
The derivative of x is 1:
0 = 1/2 (d/dx(cos(2 x)))-1
Using the chain rule, d/dx(cos(2 x)) = ( dcos(u))/( du) ( du)/( dx), where u = 2 x and ( d)/( du)(cos(u)) = -sin(u):
0 = -1+1/2-d/dx(2 x) sin(2 x)
Factor out constants:
0 = -1-1/2 sin(2 x) 2 d/dx(x)
Simplify the expression:
0 = -1-(d/dx(x)) sin(2 x)
The derivative of x is 1:
Answer: |
| 0 = -1-1 sin(2 x)