TALLER CALCULO 1

1. A) |x – 3| + |x + 2| - |x – 4| = 3

[pic 1]

[pic 2]

[pic 3]

Si 3 ≤ x < 4

x – 3 + x +2 – (- x + 4) = 3

x – 3 + x + 2 + x – 4 = 3

3x = 8

x = [pic 4]

1. Si x < 2

- x + 3 + (- x - 2) – (- x +4) = 3

- x + 3 – x – 2 + x – 4 = 3

-x – 3 = 3

x = - 6

1. Si 2 ≤ x < 3

- x + 3 + x + 2 – (- x + 4) = 3

- x +3 + x + 2 + x – 4 = 3

x + 1 = 3

x = 2

1. Si x ≥ 4

x – 3 + x + 2 – (x – 4) = 3

x – 3 + x + 2 – x + 4 = 3

x + 3 = 3

x = 0

C.S = {-6, 2}

b)                        [pic 5]

1 – 2x = 1(3 - |x – 1|)                                                                2x + 2 ≥ 0

1 – 2x = 3 - |x – 1|                                                                       2x ≥ - 2  

- |x – 1| = 1 – 2x – 3         x ≥ [pic 6]

- |x – 1| = - 2x – 2         x ≥ - 1

|x – 1| = 2x + 2//

x – 1 = - (2x + 2)        x -1 =2x + 2

x – 1 = - 2x – 2        x – 2x = 2 + 1

x + 2x = - 2 + 1        - x = 3

3x = - 1         x = - 3

x = [pic 7]

c)  [pic 8]

[pic 9]

[pic 10]

[pic 11]

                        [pic 12]

                    [pic 13]

1. El polinomio P(x) =  tiene raices  r1= 1 y r2 = - 2[pic 14]

Determine la tercera raiz

r1 = 1    r2 = -2    r3 =?

       [pic 15]

[pic 16]

                    [pic 17]

                         [pic 18]

                         [pic 19]

1. Hallar el dominio de la funcion [pic 20]

[pic 21]

[pic 22]

Dom=[pic 23]

Dom=(∞, - 3) U (- 3, 1)

1. [pic 24]

[pic 27]

1.                          [pic 28][pic 29]

[pic 30]

[pic 31]

[pic 32]

[pic 33]

[pic 34]

[pic 35]

[pic 36]

[pic 37]

[pic 38]

              [pic 39][pic 40]

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