Hoja De Trabajo Laboratorio De Matematica Basica 1

Ejercicio No 1



F(x)= X2 + 1 [pic]

Domino (-∞,∞) rango [1,∞)



F(x)=2·x

[pic]

Domino (-∞,∞) rango (∞,∞)



F(x)= 2-x2[pic]

Domino (-∞,∞) rango [2,-∞)













EJERCICIO No 2

f·x = 3·x + 2

f·a = 3·a + 2

f(x)=x2+1

f(a)=x2+1

f·x = 3 - 5·x + 4·x2

f·x = 3 - 5·a + 4·a2



EJERCICIO 3.f·x = 1 - x

f·x = 1 - x

1 – x

[pic]

Dominio (-∞,∞) Rango (-∞,∞) Decrece (∞,-∞)



X2 - 4·x

[pic]

Dominio (-∞,∞) Rango[-4,∞)
Crece [-4,∞) Decrece (∞,-4]








X2 - 4·x + 4[pic]

Dominio (-∞,∞) Rango [0,∞)
Crece [0,∞) Decrece (∞,0]


EJERCICIO 4

F(x)=3

[pic]



F(x)=-x2

[pic]



F(x)=x3-8

[pic]







EJERCICIO No. 5

10(2.73·v3 )·⎯⎯⎯⎯⎯

v – 5

[pic]

EJERCICIO No. 6

d = √(x·12 + x·22 )

d·t = √(20·t2 + 15·t2 )

d·t = √(35·t2 )

d·t = √35·t

√35·t

[pic]

EJERCICIONo. 7

2a = π·r2

a /π = r 2

r·a = √(a/π)

⎛ a ⎞1/2

r·a = (a/π)1/2











EJERCICIO No. 8

p = 2·x + 2·w

a = x·w

20 = 2·x + 2·w

20 - 2·x = 2·w

20 -2·x

w = ⎯⎯⎯⎯⎯⎯⎯⎯

2

w = 10 – x

a = x·(10 - x)



EJERCICIO No. 9

y = 40·t - 16·t2

SOLVE(40·t - 16·t2 , t, Real)

t = 2.5 ∨ t = 0

h·t = v·t -1/2·g·t2

h =40·2.5 –(1/2)·9.81·2.52

h = 2219/32

h = 69.34375

















EJERCICIO No. 10

F(X)= X3 - x

SOLVE(x3 - x, x, Real)

x = -1 ∨ x = 1 ∨ x = 0

maximo en y=0.3847 x= 0.5670minimo y=-0.387 x=-0.5670








F(x)= 3 + x + x2 - x3

SOLVE(3 + x + x2 - x3 , x, Real)

maximo en y=3.9886 x= 0.9549
minimo y=2.8161 x=1.0743

F(x)=x 5 - 8·x3·20·x

X5 - 160·x4

SOLVE(x5 - 160·x4 , x, Real)

x = 160 ∨ x = 0

5 4

x - 160·x

y = x5 - 160·x4

maximo en y= 0 x= 0
minimo y= 983000000 x= 80