Matepatica Aplicada

1)

F(x) = x2

F(x) = 11

F(x) = 1

F(3) =92

F(3) = 81

tvm= Δy/Δx=(f(3)-f(1))/(3-1)= (9-1)/2=8/2=tmv=4

2)

F(x) =2x+1

F(2) =2²+1

F(2) =4+1

F(2) =5

F(5) =25+1

F(5) =32+1

F(5) =33

tvm= Δy/Δx=(f(x)-f(x))/(x-x)= (33-5)/(5-2)=28/3=tmv=9,33

3) A)

R = 5x2

R(4) =5.42

R(4) =5.16

R(4) =80

R= 5x2

R= (6) =5.62

R= (6) =5.36

R= (6) = 180

tvm= Δy/Δx=(f(x)-f(x°))/(x-x°)= (180-80)/(6-4)=100/2=tmv=50

B)

R= 5x2

R=(6) 5.62

R=(6) = 5.36

R=(6) = 160

R= 5x2

R(8) = 5.82

R(8) = 5.64

R(8) = 320

tvm= Δy/Δx=(f(x)-f(x°))/(x-x°)= (320-180)/(8-6)=140/2=tmv=70

4) A)

P(3) = 3x2

P(3) = 3.32

P(3) = 3.9

P(3) = 27

P(5) = 3.52

P(5) = 3.25

P(5) = 75

tvm= Δy/Δx=(P(x)-P(x)°)/(P-P)= (75-27)/(5-3)=48/2=tmv=24

B)

P(6) = 3.62

P(6) = 3.56

P(6) = 108

P(10) =3.102

P(10) =3.100

P(10) = 300

tvm= Δy/Δx=(p(x)-p(x)°)/(p-p°)= (300-108)/(10-6)=192/4=tmv=48

5)

C = q2 + 400

C(1) = 12 + 400

C(1) = 1 + 400

C(1) = 401

C(5) = 52 + 400

C(5) = 25 + 400

C(5) = 425

tvm= Δy/Δx=(f(x)-f(x)°)/(x-x°)= (425-401)/(5-1)=24/4=tmv=6

6)A)

tvm= Δy/Δx=(f(2)-f(0))/(2-1)= (2-0)/1=2/1=tmv=2

tvm= Δy/Δx=(f(10)-f(5))/(10-5)= (10-5)/5=5/5=tmv=1

B)

Para ambos intervalos as funções são crescentes.

C)

tvm= Δy/Δx=(f(x)-f(x))/(x-x)= (11-10)/(11-10)=1/1=tmv=1

7)

F(x) = 5x2

F(x) = 2.5x1

F(x) = 10.x1

F(2) = 10.2

F(2) = 10.2

F(2) = 20

8)

Y = 3x2 + 4x - 3

Y = 3.42 + 4.4 - 3

Y + 3.16 + 4.4 - 3

Y = 48 + 16 - 3

Y = 64 - 3

Y = 61