Precálculo Ejemplos

$w (t) = 8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3}$

Paso 1

Considera la fórmula del cociente diferencial.

$\frac{f (t + h) - f t}{h}$

Paso 2

Obtén los componentes de la definición.

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Paso 2.1

Evalúa la función en $x = t + h$ .

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Paso 2.1.1

Reemplaza la variable $t$ con $t + h$ en la expresión.

$w (t + h) = 8.89 + 2.01 (t + h) - 0.0085 {(t + h)}^{2} + 0.000131 {(t + h)}^{3}$

Paso 2.1.2

Simplifica el resultado.

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Paso 2.1.2.1

Simplifica cada término.

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Paso 2.1.2.1.1

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 {(t + h)}^{2} + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.2

Reescribe ${(t + h)}^{2}$ como $(t + h) (t + h)$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 ((t + h) (t + h)) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.3

Expande $(t + h) (t + h)$ con el método PEIU (primero, exterior, interior, ultimo).

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Paso 2.1.2.1.3.1

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t (t + h) + h (t + h)) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.3.2

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t \cdot t + t h + h (t + h)) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.3.3

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t \cdot t + t h + h t + h \cdot h) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.4

Simplifica y combina los términos similares.

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Paso 2.1.2.1.4.1

Simplifica cada término.

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Paso 2.1.2.1.4.1.1

Multiplica $t$ por $t$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t^{2} + t h + h t + h \cdot h) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.4.1.2

Multiplica $h$ por $h$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t^{2} + t h + h t + h^{2}) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.4.2

Suma $t h$ y $h t$ .

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Paso 2.1.2.1.4.2.1

Reordena $t$ y $h$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t^{2} + h t + h t + h^{2}) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.4.2.2

Suma $h t$ y $h t$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 (t^{2} + 2 h t + h^{2}) + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.5

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.0085 (2 h t) - 0.0085 h^{2} + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.6

Multiplica $2$ por $- 0.0085$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 (h t) - 0.0085 h^{2} + 0.000131 {(t + h)}^{3}$

Paso 2.1.2.1.7

Usa el teorema del binomio.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 (t^{3} + 3 t^{2} h + 3 t h^{2} + h^{3})$

Paso 2.1.2.1.8

Aplica la propiedad distributiva.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000131 (3 t^{2} h) + 0.000131 (3 t h^{2}) + 0.000131 h^{3}$

Paso 2.1.2.1.9

Simplifica.

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Paso 2.1.2.1.9.1

Multiplica $3$ por $0.000131$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 (t^{2} h) + 0.000131 (3 t h^{2}) + 0.000131 h^{3}$

Paso 2.1.2.1.9.2

Multiplica $3$ por $0.000131$ .

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 (t^{2} h) + 0.000393 (t h^{2}) + 0.000131 h^{3}$

Paso 2.1.2.1.10

Elimina los paréntesis.

$w (t + h) = 8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 t^{2} h + 0.000393 t h^{2} + 0.000131 h^{3}$

Paso 2.1.2.2

La respuesta final es $8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 t^{2} h + 0.000393 t h^{2} + 0.000131 h^{3}$ .

$8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 t^{2} h + 0.000393 t h^{2} + 0.000131 h^{3}$

Paso 2.2

Reordena.

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Paso 2.2.1

Mueve $t^{2}$ .

$8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 t h^{2} + 0.000131 h^{3}$

Paso 2.2.2

Mueve $t$ .

$8.89 + 2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3}$

Paso 2.2.3

Mueve $8.89$ .

$2.01 t + 2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} + 8.89$

Paso 2.2.4

Mueve $2.01 t$ .

$2.01 h - 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} + 2.01 t + 8.89$

Paso 2.2.5

Mueve $2.01 h$ .

$- 0.0085 t^{2} - 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.6

Mueve $- 0.0085 t^{2}$ .

$- 0.017 h t - 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.7

Mueve $- 0.017 h t$ .

$- 0.0085 h^{2} + 0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.8

Mueve $- 0.0085 h^{2}$ .

$0.000131 t^{3} + 0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.9

Mueve $0.000131 t^{3}$ .

$0.000393 h t^{2} + 0.000393 h^{2} t + 0.000131 h^{3} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.10

Mueve $0.000393 h t^{2}$ .

$0.000393 h^{2} t + 0.000131 h^{3} + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.2.11

Reordena $0.000393 h^{2} t$ y $0.000131 h^{3}$ .

$0.000131 h^{3} + 0.000393 h^{2} t + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

Paso 2.3

Obtén los componentes de la definición.

$w (t + h) = 0.000131 h^{3} + 0.000393 h^{2} t + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

$w (t) = 8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3}$

$w (t + h) = 0.000131 h^{3} + 0.000393 h^{2} t + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89$

$w (t) = 8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3}$

Paso 3

Inserta los componentes.

$\frac{w (t + h) - w t}{h} = \frac{0.000131 h^{3} + 0.000393 h^{2} t + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3})}{h}$

Paso 4

Simplifica.

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Paso 4.1

Simplifica el numerador.

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Paso 4.1.1

Factoriza $0.000001$ de $0.000131 h^{3} + 0.000393 h^{2} t + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3})$ .

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Paso 4.1.1.1

Reordena la expresión.

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Paso 4.1.1.1.1

Mueve $h^{2}$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 h t^{2} + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3})}{h}$

Paso 4.1.1.1.2

Mueve $h$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 h t - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3})}{h}$

Paso 4.1.1.1.3

Mueve $h$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3})}{h}$

Paso 4.1.1.1.4

Mueve $8.89$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (2.01 t - 0.0085 t^{2} + 0.000131 t^{3} + 8.89)}{h}$

Paso 4.1.1.1.5

Mueve $2.01 t$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (- 0.0085 t^{2} + 0.000131 t^{3} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.1.6

Reordena $- 0.0085 t^{2}$ y $0.000131 t^{3}$ .

$\frac{0.000131 h^{3} + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.2

Factoriza $0.000001$ de $0.000131 h^{3}$ .

$\frac{0.000001 (131 h^{3}) + 0.000393 t h^{2} + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.3

Factoriza $0.000001$ de $0.000393 t h^{2}$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000393 t^{2} h + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.4

Factoriza $0.000001$ de $0.000393 t^{2} h$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000131 t^{3} - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.5

Factoriza $0.000001$ de $0.000131 t^{3}$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) - 0.0085 h^{2} - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.6

Factoriza $0.000001$ de $- 0.0085 h^{2}$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) - 0.017 t h - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.7

Factoriza $0.000001$ de $- 0.017 t h$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) - 0.0085 t^{2} + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.8

Factoriza $0.000001$ de $- 0.0085 t^{2}$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 2.01 h + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.9

Factoriza $0.000001$ de $2.01 h$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 2.01 t + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.10

Factoriza $0.000001$ de $2.01 t$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 8.89 - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.11

Factoriza $0.000001$ de $8.89$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) - (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)}{h}$

Paso 4.1.1.12

Factoriza $0.000001$ de $- (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89)$ .

$\frac{0.000001 (131 h^{3}) + 0.000001 (393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.13

Factoriza $0.000001$ de $0.000001 (131 h^{3}) + 0.000001 (393 t h^{2})$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2}) + 0.000001 (393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.14

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2}) + 0.000001 (393 t^{2} h)$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h) + 0.000001 (131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.15

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h) + 0.000001 (131 t^{3})$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3}) + 0.000001 (- 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.16

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3}) + 0.000001 (- 8500 h^{2})$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2}) + 0.000001 (- 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.17

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2}) + 0.000001 (- 17000 t h)$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h) + 0.000001 (- 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.18

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h) + 0.000001 (- 8500 t^{2})$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2}) + 0.000001 (2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.19

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2}) + 0.000001 (2010000 h)$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h) + 0.000001 (2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.20

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h) + 0.000001 (2010000 t)$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t) + 0.000001 (8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.21

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t) + 0.000001 (8890000)$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.1.22

Factoriza $0.000001$ de $0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000) + 0.000001 (- 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 1000000 (0.000131 t^{3} - 0.0085 t^{2} + 2.01 t + 8.89))}{h}$

Paso 4.1.2

Aplica la propiedad distributiva.

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 1000000 (0.000131 t^{3}) - 1000000 (- 0.0085 t^{2}) - 1000000 (2.01 t) - 1000000 \cdot 8.89)}{h}$

Paso 4.1.3

Simplifica.

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Paso 4.1.3.1

Multiplica $0.000131$ por $- 1000000$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 131 t^{3} - 1000000 (- 0.0085 t^{2}) - 1000000 (2.01 t) - 1000000 \cdot 8.89)}{h}$

Paso 4.1.3.2

Multiplica $- 0.0085$ por $- 1000000$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 131 t^{3} + 8500 t^{2} - 1000000 (2.01 t) - 1000000 \cdot 8.89)}{h}$

Paso 4.1.3.3

Multiplica $2.01$ por $- 1000000$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 131 t^{3} + 8500 t^{2} - 2010000 t - 1000000 \cdot 8.89)}{h}$

Paso 4.1.3.4

Multiplica $- 1000000$ por $8.89$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 131 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 - 131 t^{3} + 8500 t^{2} - 2010000 t - 8890000)}{h}$

Paso 4.1.4

Resta $131 t^{3}$ de $131 t^{3}$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h - 8500 t^{2} + 2010000 h + 2010000 t + 8890000 + 8500 t^{2} - 2010000 t - 8890000)}{h}$

Paso 4.1.5

Suma $- 8500 t^{2}$ y $8500 t^{2}$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 2010000 t + 8890000 - 2010000 t - 8890000)}{h}$

Paso 4.1.6

Resta $2010000 t$ de $2010000 t$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t + 8890000 - 8890000)}{h}$

Paso 4.1.7

Resta $8890000$ de $8890000$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t + 0)}{h}$

Paso 4.1.8

Suma $131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t$ y $0$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t)}{h}$

Paso 4.1.9

Reescribe $131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 t^{3} - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t$ en forma factorizada.

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Paso 4.1.9.1

Multiplica $0$ por $t^{3}$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 - 8500 h^{2} - 17000 t h + 0 t^{2} + 2010000 h + 0 t)}{h}$

Paso 4.1.9.2

Multiplica $0$ por $t^{2}$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 - 8500 h^{2} - 17000 t h + 0 + 2010000 h + 0 t)}{h}$

Paso 4.1.9.3

Multiplica $0$ por $t$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 - 8500 h^{2} - 17000 t h + 0 + 2010000 h + 0)}{h}$

Paso 4.1.9.4

Suma $131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 - 8500 h^{2} - 17000 t h + 0 + 2010000 h$ y $0$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h + 0 - 8500 h^{2} - 17000 t h + 0 + 2010000 h)}{h}$

Paso 4.1.9.5

Suma $131 h^{3}$ y $0$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h - 8500 h^{2} - 17000 t h + 0 + 2010000 h)}{h}$

Paso 4.1.9.6

Suma $131 h^{3}$ y $0$ .

$\frac{0.000001 (131 h^{3} + 393 t h^{2} + 393 t^{2} h - 8500 h^{2} - 17000 t h + 2010000 h)}{h}$

Paso 4.1.9.7

Factoriza $h$ de $131 h^{3} + 393 t h^{2} + 393 t^{2} h - 8500 h^{2} - 17000 t h + 2010000 h$ .

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Paso 4.1.9.7.1

Factoriza $h$ de $131 h^{3}$ .

$\frac{0.000001 (h (131 h^{2}) + 393 t h^{2} + 393 t^{2} h - 8500 h^{2} - 17000 t h + 2010000 h)}{h}$

Paso 4.1.9.7.2

Factoriza $h$ de $393 t h^{2}$ .

$\frac{0.000001 (h (131 h^{2}) + h (393 t h) + 393 t^{2} h - 8500 h^{2} - 17000 t h + 2010000 h)}{h}$

Paso 4.1.9.7.3

Factoriza $h$ de $393 t^{2} h$ .

$\frac{0.000001 (h (131 h^{2}) + h (393 t h) + h (393 t^{2}) - 8500 h^{2} - 17000 t h + 2010000 h)}{h}$

Paso 4.1.9.7.4

Factoriza $h$ de $- 8500 h^{2}$ .

$\frac{0.000001 (h (131 h^{2}) + h (393 t h) + h (393 t^{2}) + h (- 8500 h) - 17000 t h + 2010000 h)}{h}$

Paso 4.1.9.7.5

Factoriza $h$ de $- 17000 t h$ .

$\frac{0.000001 (h (131 h^{2}) + h (393 t h) + h (393 t^{2}) + h (- 8500 h) + h (- 17000 t) + 2010000 h)}{h}$

Paso 4.1.9.7.6

Factoriza $h$ de $2010000 h$ .

$\frac{0.000001 (h (131 h^{2}) + h (393 t h) + h (393 t^{2}) + h (- 8500 h) + h (- 17000 t) + h \cdot 2010000)}{h}$

Paso 4.1.9.7.7

Factoriza $h$ de $h (131 h^{2}) + h (393 t h)$ .

$\frac{0.000001 (h (131 h^{2} + 393 t h) + h (393 t^{2}) + h (- 8500 h) + h (- 17000 t) + h \cdot 2010000)}{h}$

Paso 4.1.9.7.8

Factoriza $h$ de $h (131 h^{2} + 393 t h) + h (393 t^{2})$ .

$\frac{0.000001 (h (131 h^{2} + 393 t h + 393 t^{2}) + h (- 8500 h) + h (- 17000 t) + h \cdot 2010000)}{h}$

Paso 4.1.9.7.9

Factoriza $h$ de $h (131 h^{2} + 393 t h + 393 t^{2}) + h (- 8500 h)$ .

$\frac{0.000001 (h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h) + h (- 17000 t) + h \cdot 2010000)}{h}$

Paso 4.1.9.7.10

Factoriza $h$ de $h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h) + h (- 17000 t)$ .

$\frac{0.000001 (h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t) + h \cdot 2010000)}{h}$

Paso 4.1.9.7.11

Factoriza $h$ de $h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t) + h \cdot 2010000$ .

$\frac{0.000001 (h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t + 2010000))}{h}$

$\frac{0.000001 h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t + 2010000)}{h}$

Paso 4.2

Simplifica los términos.

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Paso 4.2.1

Cancela el factor común de $h$ .

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Paso 4.2.1.1

Cancela el factor común.

$\frac{0.000001 h (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t + 2010000)}{h}$

Paso 4.2.1.2

Divide $0.000001 (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t + 2010000)$ por $1$ .

$0.000001 (131 h^{2} + 393 t h + 393 t^{2} - 8500 h - 17000 t + 2010000)$

Paso 4.2.2

Aplica la propiedad distributiva.

$0.000001 (131 h^{2}) + 0.000001 (393 t h) + 0.000001 (393 t^{2}) + 0.000001 (- 8500 h) + 0.000001 (- 17000 t) + 0.000001 \cdot 2010000$

Paso 4.3

Simplifica.

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Paso 4.3.1

Multiplica $131$ por $0.000001$ .

$0.000131 h^{2} + 0.000001 (393 t h) + 0.000001 (393 t^{2}) + 0.000001 (- 8500 h) + 0.000001 (- 17000 t) + 0.000001 \cdot 2010000$

Paso 4.3.2

Multiplica $393$ por $0.000001$ .

$0.000131 h^{2} + 0.000393 (t h) + 0.000001 (393 t^{2}) + 0.000001 (- 8500 h) + 0.000001 (- 17000 t) + 0.000001 \cdot 2010000$

Paso 4.3.3

Multiplica $393$ por $0.000001$ .

$0.000131 h^{2} + 0.000393 (t h) + 0.000393 t^{2} + 0.000001 (- 8500 h) + 0.000001 (- 17000 t) + 0.000001 \cdot 2010000$

Paso 4.3.4

Multiplica $- 8500$ por $0.000001$ .

$0.000131 h^{2} + 0.000393 (t h) + 0.000393 t^{2} - 0.0085 h + 0.000001 (- 17000 t) + 0.000001 \cdot 2010000$

Paso 4.3.5

Multiplica $- 17000$ por $0.000001$ .

$0.000131 h^{2} + 0.000393 (t h) + 0.000393 t^{2} - 0.0085 h - 0.017 t + 0.000001 \cdot 2010000$

Paso 4.3.6

Multiplica $0.000001$ por $2010000$ .

$0.000131 h^{2} + 0.000393 (t h) + 0.000393 t^{2} - 0.0085 h - 0.017 t + 2.01$

Paso 4.4

Mueve $- 0.0085 h$ .

$0.000131 h^{2} + 0.000393 t h + 0.000393 t^{2} - 0.017 t - 0.0085 h + 2.01$

Paso 4.5

Mueve $0.000131 h^{2}$ .

$0.000393 t h + 0.000393 t^{2} + 0.000131 h^{2} - 0.017 t - 0.0085 h + 2.01$

Paso 4.6

Reordena $0.000393 t h$ y $0.000393 t^{2}$ .

$0.000393 t^{2} + 0.000393 t h + 0.000131 h^{2} - 0.017 t - 0.0085 h + 2.01$

Paso 5