Derivadas

Questao 1

A ) (3x-4 + 23x2 - 2x + 7)dx =

(3x-4 + 23x2 - 2x + 7)dx = 3x-4dx + 2/3x2dx - 2xdx+7dx

(3x-4 + 23x2 - 2x + 7)dx = 3∫xˉ⁴dx + 2/3∫x²dx - 2∫xdx + 7∫dx
(3x-4 + 23x2 - 2x + 7)dx = ( 3*xˉ⁴⁺¹/- 4 + 1) + (2/3*x²⁺¹/2 + 1) - (2*x¹⁺¹/1 + 1) + (7*x)

(3x-4 + 23x2 - 2x + 7)dx = 3xˉ³/-3+2/3*3x³-2x²/2 + 7x + C
(3x-4 + 23x2 - 2x + 7)dx = -xˉ³+2/9x³-2x²/2 + 7x + C
(3x-4 + 23x2 - 2x + 7)dx = -1/x³ + 2x³/9-x² + 7x + C

B) 53x2 dx =

∫ 53x2 dx = 5 ∫3x2 dx ∫ 53x2 dx = 5 ∫ x23 dx ∫ 53x2 dx = 5 x23⁺¹/2/3 + 1 + C ∫ 53x2 dx = 5*x53/5/3 + C ∫ 53x2 dx = 5* (3/5) x53+ C ∫ 53x2 dx = 3 x53+ C ∫ 53x2 dx = 3 3x5 + C

Questao 2
A) 24( 2x3)dx = 24(2x3) dx = ∫2x3dx ∫2x3dx = 2(x3⁺1 /3+1 ) + C ∫2x3dx = 2 x4 / 4

F ( x ) = 2/4*(x4 )

abFx dx=F b –F(a )
F ( 4 ) = 2/4* 4⁴
F ( 4 ) = 0,5 * 256
F ( 4 ) = 128

F( 2 ) = 2/4* 2⁴
F( 2 ) = 0,5 * 16
F (2 ) = 8

24(2x3) dx = 128 - 8 = 120

B) 12( 3x2 - 2x )dx = ∫ ( 3x2-2x ) dx = 3 *( x²⁺¹/2+1) - 2 *( x¹⁺¹/1 + 1 ) + C ∫ ( 3x2-2x ) dx = 3* x³ /3 - 2*x² / 2 + C ∫ ( 3x2-2x ) dx = x³- x² + C F( x ) = x³- x² F (2) = 2³- 2² F (2) = 8 - 4 = 4 F (1) = 1³- 1² = 0

12(3x2-2x) dx= 4-0 = 4
Questao 3

RT∫ = (800-2x²) dx

RT = ∫800 dx - ∫2x² dx
RT = 800∫dx - 2∫x² dx
RT = 800x - 2*( x²⁺¹/2 + 1)
RT = 800x - 2*(x³/3) + C
RT = 800x - 2x³/3 + C

RT ( x=6) = 800*6 - 2*6³/3
RT = 4800 - 144

RT = 4.656

Questao 4

dc = (20 - 0,8 x³) dx ∫ Dc = ∫( 20 - 0,8 x³ ) dx
C( x ) = ∫20 dx - ∫0,8x³ dx
C( x ) = 20∫dx - 0,8∫x³dx
C( x ) = 20x - 0,8 *(x³⁺¹/3 + 1 ) + K
C( x ) = 20x - 0,8 ( x⁴/4 ) + K
C( x ) = 20x - 0,2x⁴ + K

C( 0 ) = 20*0 - 0,2*0⁴ + 2000

C( x )= 2000 + 20x - 0,2x⁴

Questao 5

x+2y+z=82x-y+z=33x+y-z=2

A =1212-1131-1 B = 832

det ( A ) = 1212-1131-1 122-131

det ( A ) = 1 + 6 + 2 + 3 – 1 + 4 det ( A ) = 15

X1 = x = 8213-1121-1 823-121

X1 = X =