Question

Помогите, срочно!!! .................................

Answer 1

Ответ:

Пошаговое объяснение:

1 . sin(π/6 + x) - 1/2 cosx = sinπ/6 cosx + sinx cosπ/6 - 1/2 cosx = 1/2 cosx + √3/2 sinx -

- 1/2 cosx = √3/2 sinx .

2 . 1 - √2 sin2x = 0 ;

√2 sin2x = 1 ;

sin2x = √2 /2 ;

2x = ( - 1 )ⁿarcsin( √2 /2) + πn , nЄ Z ;

2x = ( - 1 )ⁿ π/4 + π n , nЄ Z ;

x = ( - 1 )ⁿ π/8 + (π n)/2 , nЄ Z ;

3 . a ) y = x³/3 + x²/2 - 12 ; y' = ( x³/3 + x²/2 - 12 )' = 3x²/3 +2x/2 -0 = x² + x ;

y' = x² + x ;

б ) y = cos ( 1 - 4x ) ; y' = ( cos ( 1 - 4x ) )' = - sin ( 1 - 4x ) * ( 1 - 4x )' = 4sin ( 1 - 4x ) ;

y' = 4sin ( 1 - 4x ) .

4 . y = x³ - 3x² + 3x + 2 ; x Є [ - 2 ; 2 ] ;

y ' = 3x² - 6x +3 = 3 ( x² - 2x + 1 ) = 3 ( x - 1 )² ;

y ' = 0 ; 3 ( x - 1 )²= 0 ;

x = 1 - критична точка ; 1Є [ - 2 ; 2 ] ;

y ( - 2 ) = (- 2 )³ - 3 ( - 2 )² + 3* ( - 2 ) + 2 = - 8 - 12 - 6 + 2 = - 24 ;

y ( 1 ) = 1³ - 3 * 1² + 3 * 1 + 2 = 1 - 3 + 3 + 2 = 3 ;

y ( 2 ) = 2³ - 3 * 2² + 3 * 2 + 2 = 8 - 12 + 6 + 2 = 4 ;

max y(x) = 4 ; min y(x) = - 24 ;

[ - 2;2] [ - 2;2]

5 . S пов = S б + 2S осн ;

AC = 5 ; BC = 12 ; за т. Піфагора АВ = √ ( 5² + 12²) = √ 169 = 13 ;

Р осн = 5 + 12 + 13 = 30 ; S б = Р осн*H = 30 * 8 = 240 ; S б = 240 ;

2S осн = 2 * (1/2 * 5 * 12 ) = 60 ;

S пов = 240 + 60 = 300 ( кв. од. ) .