ED CGA unip

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(1) B
(2)
A
T=A.L+B
35=-0,5.0
B=35
T=-0,5L+35
A=delta(t)/delta(L)
5-35/60-0
A= -30/60
A=-0,5
(3) D
(4)
E
IB=T^2-24T+143
IB=2T-24
0=2T-24
24=2T
24/2=T
T=12h
IB=T^2-24T+143
IB=(12^2-24(12)+143
IB= -1
(5)
E
AB=B-A
AB=(1-4)-(-2,3)
AB=(1,-4)+(2,-3)
AB=(3,-7)
(6)
B
U.V=/U/./V/.COS=6.9COS 150 Graus=54(-raiz quadrada 3/2)= -27raiz quadrada3
(7) B 
SOMA DE VETORES
(8) 
C
U.V
(5,2-1).(-4,2,1)=-20+4-1= -17
(9)
A
V(t)=15t^2-750t+9000
V(3)=15.3^2-750.3+9000
V(3)=6885 L
(10)
E
V(t)= 15t^2-750t+9000
V(t)=30t-750
V(3)=30(3)-750
V(3)= -660 l/h
(11) 
D
V(t)=0
V(t)= -4,5t^2+18t
V(t)= -9t+18
0= -9t+18
9t=18
T=18/9
T=2s
V(t)= -4,5t^2+18t
V(2)= -4,5(2)^2+18(2)
V(2)=-18+36
V(2)=18m/S
12)
A
/U/=RAIZ (-3)^2+4^2+0^2= RAIZ DE 25=5
(II)-0,6/-3=0,8/4=0/0
0,2=0,2 MESMO SENTIDO
/VETOR/=RAIZ QUADRADA(-06)^2+0,8^2+0^2
/VETOR/=RAIZ QUADRADA 0,36+0,64=RAIZ QUADRADA 1 
/VETOR/=1
(III) 9/-3=-12/4=0
-3=-3
/Vetor/=Raiz quadrada 9^2+(-12)^2+0^2
/Vetor/= Raiz quadrada 81+144= raiz quadrada 225
/Vetor/=15
13)
A
W=XU+BV
(-17,12)=X(-2,0)+B(3-4) -2X+3B=-17
(-17,12)=(-2X,0)+(3B,-4B) -2X+3(-3)= -17
(-17,12)=(-2X+3B,-4B) -2X-9=-17
-2X+3B-17 -9+17=2X
-4B=12 8/2=X
B=12/-4 X=4
B=-3
14)
A
AO+DE+PL+FQ+IH
AO+DE+FQ
AO+OD+DP=AP
15)
E
AQ=AE+EG+GQ
AQ=AE+EG+2/3GH
AQ=AE=+AC+23AB
D
I)
2U – 4V = 2(1,-2)-4(-4,0)
 2U-4U = (2-4)+(16,0)
2U-4U = (18,-4)
II) 
U+V=(1,-2)+(-4,0) = (-3,-2)
| U+V| = RAIZ (-3)^2 + (-2)^2 = RAIZ 13
(III)
XU/XV=YU/YV
1/-4=-2/0
Não é verdadeira U diferente de V
17)
B
XU/ XV = YU/YV
(X+12)/6 = 3/9 
9(X+12) = 18
9X+108=18
9X=18-108
X=-90/9
X=-10
18)
D
|S |= RAIZ( 3^2 +(-6)^2)
|S| = RAIZ (9+36)
|S| = RAIZ 45
|S| = 3 RAIZ 5
19)
B
AB=B-A
AB=(0,-4)-(-1,3)
AB=(0,-4)-(1-3)
AB=(1-7)
|AB |= RAIZ 1^2+7^2
|AB|=RAIZ50=5RAIZ 2
U=(-4,28)
20)
B
|AB|=RAIZ quadrada (-1^2+12 = RAIZ 2
AB= AB / |AB| = (-1,1) / RAIZ 2 . RAIZ 2 / RAIZ 2
AB=(-1,1)*RAIZ 2)/2
AB=(-RAIZ 2 / RAIZ 2 , RAIZ 2/ RAIZ 2)
21)
C
V(t) = 18t^2+1,5t
V(2) = 6*(2)^3+1,5(2)
V(2)= 51L
22)
B
V’(t) = 18t^2+1,5
V’(2) = 18(2)~2 +1,5
V’(2) = 73,5L/min
23)
B
U = X+16 V = SEM X 
U’ = 1 V’ = COS X 
Y’ = 1SENX + (X+16)*COS X
Y’ = SEM X + (X+16)*COSX
24)
A 
A= f ´ (X) = 3X^2 
A = 3X^2
A = 3(-2) ^2 
A = 12
25)
A
U = e ^X V= SEN(2X)
U´= e^2 V´ = 2 COS (2X)
f ´(X) = e^X SEN 2X)+ e^X (2COS(2X))
f´(x) = e^X | SEN2X)+2COS(2X))|
f`(0 )= e^0 |SEN (2.0)+2 COS (2*0)|
f´(0) = 2
26)
E
U*V = (2,-4) * (0,-3)
= 12
27)
C
2U = 2(2,-4) = (4,-8) 5V = 5(1,-2) = (5,-10)
2U * 5V
(4,-8)* (5,-10) 
20+80
100
28) 
A
A=/uv/ 
I j k i j
2 -4 2 2 -4
1 -4 0 1 -4
· - - +++ 
u v= oi 2j -8k
 8i-oj 4R
uv= 8i +2j-4k
/uv/= raiz quadrada 8^2+2^2(-4)^2
A=raiz quadrada 64+4+16=raiz quadrada84
A= 2raiz de 21
29)
E
A= | U ^ V | = | U| *|V| SEN Ø 
A = (2*3*SEN 30º ) / 2
A = 1,5
30)
B
w _|_ U => W*U = 0
=> (2,-4,10) *( 1,-2,-1) 
 2+8-10 = 0
w _|_ V => W*V=0
 (2,-4,10)* (2,1,0) = 0
 (4 – 4) = 0
 0 = 0
|w| = RAIZ| 2^2 +(4)^2 +10^2 
 RAIZ 120
 2 RAIZ 30
31)
A
U*V = (1,-2,-1)* (2,1,0)
U*V = 2-2-0
U*V = 0
32)
C
|U| ^2+2U*V+U*V+2|V|^2
3^2+2*4^2 
9+32
41
33)
B
U_|_ V =0
U*V=0
(1,X,8)*(2,1,4)=0
2+X-32=0
x=32-2
x=30
34) 
A
· - - + + +
I J K I J
0 -3 -1 0 -3
2 4 0 2 4
Oi-2j+0k
4i-oj+6k
Resultdo
4i-2j+6k
U V=(4,-2,6)
35)
D
I)
f (X)= e ^CON X
f´(x) = -SENX e ^COS X 
II)
f (X) = LN (X^2 +4)
f ´(x) = 2X / X^2 +4
III)
f´ (X)= RAIZ 3X +6
f´(X) = 3/ 2RAIZ 3X+6
36)
C
(I)
f (x)=sen(2x+4)
f(x)=2cos(2x+4)
II)
f´(X) =COS (3X+6)
f´(X) = - 3SEN (3X+6)
III)
f ´(X) = (X^2 +4X)^2 * (2X+4)
f´(X) = (X^2 + 4X)^2 (6X +12)
37)
D
I)
ƒ 3X^2 dx
3X^3/3 + C 
X^3 +C
II)
ƒ 4X^3 dx
4X^4 / 4+C
X^4+C
III)
ƒ 5X^4dx = 5X^5/5 + C
X^5 +C
38)
B
S(t) = ƒ V(t) dt = ƒ (14t -6t^2)dt
S(t) = 14t^2 /2 – 6t^3/3+C 
S(t)=7t^2-2t^3+C
S(1) = 7(1)^2 -2(1)^3 +C = 16=7-2+C
16-7+2=C 
C=11 
S(t)=7t^2 -2t^3+11
39)
A
ƒ(2X+COS )DX
2X^2 / 2 +SENX +C
X^2 + SEN +C
(40)
C
ƒXe^Xdx= Xe^X-e^X+C
-