ED's de Cálculo

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

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

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
t=3,16s
tempo de queda é de aproximadamente 3,2s

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

5)Segmento AB AB=(1-(-2),-4-3)
A=(-2,3) AB=(3,-7)
B=(1,-4)

6)cos0º=1 v3=1,732 u.v.θ
45º=0,707 6.9.-0,866
90º=0 -46,764=-27v3
150º=-0,866
180º=-1

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
Resposta: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

9)V(t)=15t²-750t+9000
V(3)=15(3)²-750(3)+9000
V(3)=135-2250+9000
V(3)=6885

10)ΔV/Δt=V'=2.15t-750
V'=30t-750
V'=30.3-750
V'=90-750
V'= -660L/h

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

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
1=1
|u|=√9²+12²
|u|=√81+144
|u|=√225
|u|=15

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

14)AO+DE+PL+FQ+IH
AO+OD+DM+ML+LP
AP

15)AQ=AC+CG+GQ
AQ=AC+AE+2/3GH
AQ=AE+AC+2/3AB

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

17) x+12/6=3/9
9(x+12)=3.6
9x+108=18
9x=-108+18
9x=-90
x=-10

18) |s|=√3²+(-6)²
|s|=√9+36
|s|=√45
|s|=3√5

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

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)
|AB|
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

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'=73,5L/min

23)y=(x+16).senx



y'=u'.v+u.v'
y'=1.senx+(x+16).cosx
y'=senx+(x+16).cosx

24)f(x)=x³-8 xo=-2
y'=3x² a=f'(-2)
f'(-2)=3.(-2)²
f'(-2)=3.4
f'(-2)=12

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

26)u=(2,-4) u.v=(2.0+4.-3)
v=(0,-3) u.v=(0+12)
u.v=12

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


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

29)|u|=2 A=b.h
|v|=3 A=|u|.|v|.senθ/2
θ=30º A=2.3.0,5/2
A=1,5uA

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

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

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

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

34)u=(0,-3,-1) i j k
v=(2,4,0) 0 -2 0
4 0 6

|  j k  j | u˄v=(4,-2,6)

u˄v=|0 -3 -1 0 -3|

|  4 ; -2;  4|

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

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)

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

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


39)ʃ(2x+cosx)dx = senx+2x²/2+c
X²+senx+c


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

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