CGA EDS

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1) Agricultura atual Terra Nossa
 20-10-10 10-10-20
 100kg 300kg
 100+300=400
20+30=50 (50/400)x100=12,5%
10+30=40 (40/400)x100=10%
10+60=70 (70/400)x100=17,5%
12,5-10-17,5 B
2) a=(y2-y1)/(x2-x1) 0=-2.35+b
 a=(60-0)/(5-35) b-70=0
 a=60/-30 b=70
 a=-2 y=-2x+70
 2x=-y+70
 X=-0,5y+35 A
3) h=-4,9t2 + 49 Taxa de variação 
 Altura do prédio = 49cm dh/dt=h′(t)=-9,8t
 0=-4,9t2+49
 4,9t2=49
 t2=10
 t2=3,16s
Tempo de queda é de aproximadamente 3,2s D
4) IB(t)=t2-24t+143
 xv=-b/2a yv=-b2-4ac/4ª
xv=-(-24/2) yv=-(576-572/4)
xv=12 yv=-4/4
 yv=-1
tmin=12
IBmin=-1 E
5) Segmento AB AB=(1-(-2),-4-3)
A=(-2,3) AB=(3,-7)
B=(1,-4) E
6) cos 0° = 1 v3=1,732 u.v.θ
 45°= 0,707 6.9.-0,866
 90°= 0 -46,764=-27v3
 150°=-0,866
 180°=-1 B
7) u+v u=2i+3j-k
 v=-i+2j
 u+v=i+5j-k
 u.v u.v=2.-1i3.2j-1.0k
 u.v=-2i+6j B
8) u=5i+2j-k v=-4i+2j+k
u.v= 5.-4i2.2j-1.1k
u.v=-20i+4j-k
u.v=-20+4-1
u.v=-17 C
9) V(t)=15t2-750t+9000
 V(3)= 15(3)2-750(3)+9000
 V(3)=135-2250+9000
 V(3)=6885 A
10) ∆v/∆t=v′=2.15t-750
 v′=30t-750
 v′=30.3-750
 v′=90-750
 v′=660L/h E
11) v(t)=-4,5t2+18t
 v′=-9t+18 v(t)=-4,5.(2)2+18.2
 9t-18=0 v(t)=-18+36
 9t=18 v(t)=18m/s
 t=2s D
12) │u│= √(-3)2+42+02 -0,6/-3=0,8/4
 │u│= √9+16+0 - 0,6.4=-3.0,8
 │u│= √25 -2,4=-2,4
 │u│= 5
 1=√(-0,6)2 + 0,82 9/-3=-12/4
 1=√0,36+0,64 4.9=-12.-3
 1=√1 36=36
 │u│=√92+122
 │u│=√81+144
 │u│= √225
 │u│= 15 A
13) w=α.u+β.v
 (-17,12)=α.(-2,0)+β.(3,-4)
 (-17,12)=-2α+3β;-4β+0
 -4β=12 -2α+3β=-17
 -β=3 -2α+3.-3=-17
 β=-3 -2α=-17+9
 -2α=-8
 α=4 A
14) AO+DE+PL+FQ+IH
 AO+OD+DM+ML+LP
 AP A
15) AQ=AC+CG+GQ
 AQ=AC+AE+2/3GH
 AQ=AE+AC+2/3AB E
16) u=(1,-2) 2u=(2,-4)
 V=(-4,0) 4v=(-16,0)
 2u-4v=(2-(-16).-4-0)
 2u-4v=(18.-4)
u=(1,-2) │u+v│=√(-3)2+(-2)2
v=(-3,0) │u+v│=√9+4
u+v=(-3,-2) │u+v│=√13
 1/4=-2/0
8≠0 D
17) x+12/6=3/9
 9(x+12)=3.6
 9x+108=18
 9x=-108+18
 9x=-90
 X=-10 B
18) │s│=√32+(-6)2
 │s│=√9+36
 │s│=√45
 │s│= 3√5 D
19) AB=(x2-x1,y2-y1) A(-1,3) B(0,-4)
 AB=(0-(-1),-4-3)
 AB=(1,-7)
 1/4=-7/28
 1.28=-4.-7
 28=28 B
20) AB=(x2-x1,y2-y1) A=(-1,0) B(-2,1)
 AB=(-2-(-1),1-0)
 AB=(-1,1)
 │AB│=√(-1)2+12 AB/│AB│=(-1/√2, 1/√2)
 │AB│=√1+1 AB/│AB│=(-1.√2/√2.√2,1.√2/√2.√2)
 │AB│=√2 AB/│AB│=(-√2/2,√2/2)
 B
21) V(t)=6t3+1,5t
 V(t)=6.23+1,5.2
 V(t)=6.8+3
 V(t)=48+3
 V(t)=51 C
22) V(t)=6.t3+1,5t
 V′=3.6t2+1,5
 V′=18t2+1,5
 V′=18.22+1,5
 V′=18.4+1,5
 V′=72+1,5
 V′=73,5 L/min B
23) y=(x+16).senx
 y′=u′.v+u.v′
 y′=1.senx+(x+16).cosx
 y′=senx+(x+16).cosx B
24) f(x)=x3-8 xo=-2
 y′=3x2 a=f′(-2)
 f′(-2)=3.(-2)2
 f′(-2)=3.4
 f′(-2)=12 A
25) f(x)=ex.sen(2x) u=2x 
 f′(x)=(ex.senu+ex.cosu).u′ u=2
 f′(x)=((ex.(senu+cosu)).u′
 f′(x)=((ex′(sen2x+cos2x)).2
 f′(0)=((e0.(sen2.0+cos2.0)).2
 f′(0)=((1.(0+1)).2
 f′(0)=1.2
 f′(0)=2 A
26) u=(2,4) u.v=(2.0+4.-3)
 v=(0,3) u.v=(0+12)
 u.v=12 E
27) u=(2,-4) 2.u=(2.2,2-4) 2u(4,-8)
 v=(1,-2) 5.v=(5.1,5.-2) 5v(5,-10)
 2u.5v=(4.5+(-8.-10))
 2u.5v=(20+80)
 2u.5v=100 C
28) u=(2,-4,2) A=│u˄v│
 v=(1,-4,0)
 |ij k i j| ijk
|u˄v|=|1-40 1-4| -80-4
 |2-42 2-4| - (0-28)
 (-8,-2,4)
A=|(-8,-2,4)|=√(-8)²+(-2)²+4²=√84
A=2˄√21 A 
 
29) |u|=2 A=b.h
 |v|=3 A=|u|.|v|.senθ/2
 θ=30º A=2.3.0,5/2
 A=1,5uA E
30) u=(1,-2,-1)
 v=(2,1,0)
w.u=0 (a,b,c).(1,-2,-1)=a-2b-c=0
w.v=0 (a,b,c).(2,1,0)=2a+b =0
a-2b-c=0 w=√2²+(-4)²+10²=2√30
2a+b =0 w=√4+16+100=2√30
a²+b²+c²=2√30 w=√120=2√30
 w=2√30=2√30
2a+b=0 a-2b-c=0
2.2-4=0 2-(-2.-4)-10=0 w=(2,-4,10)
0=0 2+8-10=0 |w|=2√30
 0=0 B
31) u=(1,-2,-1)
 v=(2,1,0)
 u.v=(1.2+(-2.1)+(-1.0))
 u.v=(2-2+0)
 u.v=0 A
32) |u|=3(u+v).(u+2v)
 |v|=4 u²+2.v.u+u.v+2.v²
 3²+2.0+0+2.4²
 9+0+0+32
 41 C
33) u=(1,x,8)
 v=(2,1,-4)
 u.v=0
 (1.2+x.1+(8.-4)=0
 (2+x-32)=0
 x-30=0
 x=30 B
 34) u=(0,-3,-1) i j k
 v=(2,4,0) 0-2 0
 4 0 6
 | i j k i j | u˄v=(4,-2,6)
 u˄v=|0-3-1 0-3|
 | 2 4 0 2 4| A
35) f(x)=e(cosx)
u=cosx u'=-senx
f'(x)=e(u).u'
f'(x)=-senx.e(cosx)
f(x)=ln(x²+4) u'=2x
u=x²+4
f(x)=ln(u)
f(x)=1/u.u'
f'(x)=1/x²+4.2x
f'(x)=2x/x²+4
f(x)=√3x+6 u'=3
f(x)=(3x+6)1/2 f(x)=3/2.1/u1/2
u=3x+6 f(x)=3/2√3x+6
f'(x)=(u)1/2
f'(x)=1/2.u-1/2.u'
f'(x)=3/2.u-1/2 D
36) f(x)=sen(2x+4) u'=2
u=2x+4
f(x)=sen(u)
f'(x)=cos(u).u'
f'(x)=2cos(2x+4)
f(x)=cos(3x+6) u'=3
u=3x+6
f(x)=cos(u)
f'(x)=-sen(u).u'
f'(x)=-sen(3x+6).3
f'(x)=-3sen(3x+6)
f(x)=(x²+4x)³
u=x²+4x u'=2x+4
f(x)=(u)³
f'(x)=3u².2x+4
f'(x)=3(x²+4x).2x+4
f'(x)=(x²+4x)².(6x+12) C
37) F(x)=x³+4 (x³+4)'=f(x)
 f(x)=3x²
 F(x)=x^4+2 (x^4+2)'=f(x)
 f(x)=4x³
 F(x)=x^5-2 (x^5-2)'=f(x)
 f(x)=5x^4 D
38) v=ds/dt=>ds=v.dt
 s=ʃv.dt
16=-2.1³+7.1²+c s=ʃ(14t-6t²).dt
16=-2+7+c s=14t²/2-6t³/3+c
16=5+c s=7t²-2t³+c
c=11 s=7t²-2t³+11 B
39) ʃ(2x+cosx)dx = senx+2x²/2+c
 X²+senx+c A
40) ʃ(senx+4)dx ʃ(1/x+12)dx f(x)=ex
 -cosx+C+4x ln|x|+c+12x (ex)'=f(x)
 -cosx+4x+C ln|x|+12x+c C