Precálculo Ejemplos

Hallar el ratio de cambio medio w(t)=8.89+2.01t-0.0085t^2+0.000131t^3
w(t)=8.89+2.01t-0.0085t2+0.000131t3w(t)=8.89+2.01t0.0085t2+0.000131t3
Paso 1
Considera la fórmula del cociente diferencial.
f(t+h)-fthf(t+h)fth
Paso 2
Obtén los componentes de la definición.
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Paso 2.1
Evalúa la función en x=t+hx=t+h.
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Paso 2.1.1
Reemplaza la variable tt con t+ht+h en la expresión.
w(t+h)=8.89+2.01(t+h)-0.0085(t+h)2+0.000131(t+h)3w(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+2.01t+2.01h-0.0085(t+h)2+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t+h)2+0.000131(t+h)3
Paso 2.1.2.1.2
Reescribe (t+h)2(t+h)2 como (t+h)(t+h)(t+h)(t+h).
w(t+h)=8.89+2.01t+2.01h-0.0085((t+h)(t+h))+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085((t+h)(t+h))+0.000131(t+h)3
Paso 2.1.2.1.3
Expande (t+h)(t+h)(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+2.01t+2.01h-0.0085(t(t+h)+h(t+h))+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(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+2.01t+2.01h-0.0085(tt+th+h(t+h))+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(tt+th+h(t+h))+0.000131(t+h)3
Paso 2.1.2.1.3.3
Aplica la propiedad distributiva.
w(t+h)=8.89+2.01t+2.01h-0.0085(tt+th+ht+hh)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(tt+th+ht+hh)+0.000131(t+h)3
w(t+h)=8.89+2.01t+2.01h-0.0085(tt+th+ht+hh)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(tt+th+ht+hh)+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 tt por tt.
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+th+ht+hh)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+th+ht+hh)+0.000131(t+h)3
Paso 2.1.2.1.4.1.2
Multiplica hh por hh.
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+th+ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+th+ht+h2)+0.000131(t+h)3
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+th+ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+th+ht+h2)+0.000131(t+h)3
Paso 2.1.2.1.4.2
Suma thth y htht.
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Paso 2.1.2.1.4.2.1
Reordena tt y hh.
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+ht+ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+ht+ht+h2)+0.000131(t+h)3
Paso 2.1.2.1.4.2.2
Suma htht y htht.
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+2ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+2ht+h2)+0.000131(t+h)3
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+2ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+2ht+h2)+0.000131(t+h)3
w(t+h)=8.89+2.01t+2.01h-0.0085(t2+2ht+h2)+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085(t2+2ht+h2)+0.000131(t+h)3
Paso 2.1.2.1.5
Aplica la propiedad distributiva.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.0085(2ht)-0.0085h2+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085t20.0085(2ht)0.0085h2+0.000131(t+h)3
Paso 2.1.2.1.6
Multiplica 22 por -0.00850.0085.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017(ht)-0.0085h2+0.000131(t+h)3w(t+h)=8.89+2.01t+2.01h0.0085t20.017(ht)0.0085h2+0.000131(t+h)3
Paso 2.1.2.1.7
Usa el teorema del binomio.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131(t3+3t2h+3th2+h3)w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131(t3+3t2h+3th2+h3)
Paso 2.1.2.1.8
Aplica la propiedad distributiva.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000131(3t2h)+0.000131(3th2)+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000131(3t2h)+0.000131(3th2)+0.000131h3
Paso 2.1.2.1.9
Simplifica.
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Paso 2.1.2.1.9.1
Multiplica 33 por 0.0001310.000131.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393(t2h)+0.000131(3th2)+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393(t2h)+0.000131(3th2)+0.000131h3
Paso 2.1.2.1.9.2
Multiplica 33 por 0.0001310.000131.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393(t2h)+0.000393(th2)+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393(t2h)+0.000393(th2)+0.000131h3
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393(t2h)+0.000393(th2)+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393(t2h)+0.000393(th2)+0.000131h3
Paso 2.1.2.1.10
Elimina los paréntesis.
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3
w(t+h)=8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3w(t+h)=8.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3
Paso 2.1.2.2
La respuesta final es 8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3.
8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3
8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3
8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393t2h+0.000393th2+0.000131h3
Paso 2.2
Reordena.
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Paso 2.2.1
Mueve t2t2.
8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393th2+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393th2+0.000131h3
Paso 2.2.2
Mueve tt.
8.89+2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h38.89+2.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3
Paso 2.2.3
Mueve 8.898.89.
2.01t+2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+8.892.01t+2.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+8.89
Paso 2.2.4
Mueve 2.01t2.01t.
2.01h-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+2.01t+8.892.01h0.0085t20.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+2.01t+8.89
Paso 2.2.5
Mueve 2.01h2.01h.
-0.0085t2-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+2.01h+2.01t+8.890.0085t20.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3+2.01h+2.01t+8.89
Paso 2.2.6
Mueve -0.0085t20.0085t2.
-0.017ht-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3-0.0085t2+2.01h+2.01t+8.890.017ht0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h30.0085t2+2.01h+2.01t+8.89
Paso 2.2.7
Mueve -0.017ht0.017ht.
-0.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h3-0.017ht-0.0085t2+2.01h+2.01t+8.890.0085h2+0.000131t3+0.000393ht2+0.000393h2t+0.000131h30.017ht0.0085t2+2.01h+2.01t+8.89
Paso 2.2.8
Mueve -0.0085h20.0085h2.
0.000131t3+0.000393ht2+0.000393h2t+0.000131h3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.890.000131t3+0.000393ht2+0.000393h2t+0.000131h30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
Paso 2.2.9
Mueve 0.000131t30.000131t3.
0.000393ht2+0.000393h2t+0.000131h3+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.890.000393ht2+0.000393h2t+0.000131h3+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
Paso 2.2.10
Mueve 0.000393ht20.000393ht2.
0.000393h2t+0.000131h3+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.890.000393h2t+0.000131h3+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
Paso 2.2.11
Reordena 0.000393h2t0.000393h2t y 0.000131h30.000131h3.
0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.890.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.890.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
Paso 2.3
Obtén los componentes de la definición.
w(t+h)=0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89w(t+h)=0.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
w(t)=8.89+2.01t-0.0085t2+0.000131t3w(t)=8.89+2.01t0.0085t2+0.000131t3
w(t+h)=0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89w(t+h)=0.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89
w(t)=8.89+2.01t-0.0085t2+0.000131t3w(t)=8.89+2.01t0.0085t2+0.000131t3
Paso 3
Inserta los componentes.
w(t+h)-wth=0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89-(8.89+2.01t-0.0085t2+0.000131t3)hw(t+h)wth=0.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89(8.89+2.01t0.0085t2+0.000131t3)h
Paso 4
Simplifica.
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Paso 4.1
Simplifica el numerador.
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Paso 4.1.1
Factoriza 0.0000010.000001 de 0.000131h3+0.000393h2t+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89-(8.89+2.01t-0.0085t2+0.000131t3)0.000131h3+0.000393h2t+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89(8.89+2.01t0.0085t2+0.000131t3).
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Paso 4.1.1.1
Reordena la expresión.
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Paso 4.1.1.1.1
Mueve h2h2.
0.000131h3+0.000393th2+0.000393ht2+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89-(8.89+2.01t-0.0085t2+0.000131t3)h0.000131h3+0.000393th2+0.000393ht2+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89(8.89+2.01t0.0085t2+0.000131t3)h
Paso 4.1.1.1.2
Mueve hh.
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017ht-0.0085t2+2.01h+2.01t+8.89-(8.89+2.01t-0.0085t2+0.000131t3)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017ht0.0085t2+2.01h+2.01t+8.89(8.89+2.01t0.0085t2+0.000131t3)h
Paso 4.1.1.1.3
Mueve hh.
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(8.89+2.01t-0.0085t2+0.000131t3)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(8.89+2.01t0.0085t2+0.000131t3)h
Paso 4.1.1.1.4
Mueve 8.898.89.
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(2.01t-0.0085t2+0.000131t3+8.89)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(2.01t0.0085t2+0.000131t3+8.89)h
Paso 4.1.1.1.5
Mueve 2.01t2.01t.
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(-0.0085t2+0.000131t3+2.01t+8.89)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.0085t2+0.000131t3+2.01t+8.89)h
Paso 4.1.1.1.6
Reordena -0.0085t20.0085t2 y 0.000131t30.000131t3.
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
0.000131h3+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000131h3+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.2
Factoriza 0.0000010.000001 de 0.000131h30.000131h3.
0.000001(131h3)+0.000393th2+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000393th2+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.3
Factoriza 0.0000010.000001 de 0.000393th20.000393th2.
0.000001(131h3)+0.000001(393th2)+0.000393t2h+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000393t2h+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.4
Factoriza 0.0000010.000001 de 0.000393t2h0.000393t2h.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000131t3-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000131t30.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.5
Factoriza 0.0000010.000001 de 0.000131t30.000131t3.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)-0.0085h2-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)0.0085h20.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.6
Factoriza 0.0000010.000001 de -0.0085h20.0085h2.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)-0.017th-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)0.017th0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.7
Factoriza 0.0000010.000001 de -0.017th0.017th.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)-0.0085t2+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)0.0085t2+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.8
Factoriza 0.0000010.000001 de -0.0085t20.0085t2.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+2.01h+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+2.01h+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.9
Factoriza 0.0000010.000001 de 2.01h2.01h.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+2.01t+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+2.01t+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.10
Factoriza 0.0000010.000001 de 2.01t2.01t.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+8.89-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+8.89(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.11
Factoriza 0.0000010.000001 de 8.898.89.
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)-(0.000131t3-0.0085t2+2.01t+8.89)h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)(0.000131t30.0085t2+2.01t+8.89)h
Paso 4.1.1.12
Factoriza 0.0000010.000001 de -(0.000131t3-0.0085t2+2.01t+8.89)(0.000131t30.0085t2+2.01t+8.89).
0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3)+0.000001(393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.13
Factoriza 0.0000010.000001 de 0.000001(131h3)+0.000001(393th2)0.000001(131h3)+0.000001(393th2).
0.000001(131h3+393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2)+0.000001(393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.14
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2)+0.000001(393t2h)0.000001(131h3+393th2)+0.000001(393t2h).
0.000001(131h3+393th2+393t2h)+0.000001(131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h)+0.000001(131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.15
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h)+0.000001(131t3)0.000001(131h3+393th2+393t2h)+0.000001(131t3).
0.000001(131h3+393th2+393t2h+131t3)+0.000001(-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t3)+0.000001(8500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.16
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3)+0.000001(-8500h2)0.000001(131h3+393th2+393t2h+131t3)+0.000001(8500h2).
0.000001(131h3+393th2+393t2h+131t3-8500h2)+0.000001(-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h2)+0.000001(17000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.17
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2)+0.000001(-17000th)0.000001(131h3+393th2+393t2h+131t38500h2)+0.000001(17000th).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th)+0.000001(-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th)+0.000001(8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.18
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th)+0.000001(-8500t2)0.000001(131h3+393th2+393t2h+131t38500h217000th)+0.000001(8500t2).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2)+0.000001(2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.19
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2)+0.000001(2010000h)0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2)+0.000001(2010000h).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h)+0.000001(2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.20
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h)+0.000001(2010000t)0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h)+0.000001(2010000t).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t)+0.000001(8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t)+0.000001(8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.21
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t)+0.000001(8890000)0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t)+0.000001(8890000).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.1.22
Factoriza 0.0000010.000001 de 0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000)+0.000001(-1000000(0.000131t3-0.0085t2+2.01t+8.89))0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000)+0.000001(1000000(0.000131t30.0085t2+2.01t+8.89)).
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+88900001000000(0.000131t30.0085t2+2.01t+8.89))h
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-1000000(0.000131t3-0.0085t2+2.01t+8.89))h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+88900001000000(0.000131t30.0085t2+2.01t+8.89))h
Paso 4.1.2
Aplica la propiedad distributiva.
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-1000000(0.000131t3)-1000000(-0.0085t2)-1000000(2.01t)-10000008.89)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+88900001000000(0.000131t3)1000000(0.0085t2)1000000(2.01t)10000008.89)h
Paso 4.1.3
Simplifica.
Toca para ver más pasos...
Paso 4.1.3.1
Multiplica 0.0001310.000131 por -10000001000000.
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-131t3-1000000(-0.0085t2)-1000000(2.01t)-10000008.89)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000131t31000000(0.0085t2)1000000(2.01t)10000008.89)h
Paso 4.1.3.2
Multiplica -0.00850.0085 por -10000001000000.
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-131t3+8500t2-1000000(2.01t)-10000008.89)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000131t3+8500t21000000(2.01t)10000008.89)h
Paso 4.1.3.3
Multiplica 2.012.01 por -10000001000000.
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-131t3+8500t2-2010000t-10000008.89)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000131t3+8500t22010000t10000008.89)h
Paso 4.1.3.4
Multiplica -10000001000000 por 8.898.89.
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-131t3+8500t2-2010000t-8890000)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000131t3+8500t22010000t8890000)h
0.000001(131h3+393th2+393t2h+131t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000-131t3+8500t2-2010000t-8890000)h0.000001(131h3+393th2+393t2h+131t38500h217000th8500t2+2010000h+2010000t+8890000131t3+8500t22010000t8890000)h
Paso 4.1.4
Resta 131t3131t3 de 131t3131t3.
0.000001(131h3+393th2+393t2h+0t3-8500h2-17000th-8500t2+2010000h+2010000t+8890000+8500t2-2010000t-8890000)h0.000001(131h3+393th2+393t2h+0t38500h217000th8500t2+2010000h+2010000t+8890000+8500t22010000t8890000)h
Paso 4.1.5
Suma -8500t28500t2 y 8500t28500t2.
0.000001(131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+2010000t+8890000-2010000t-8890000)h0.000001(131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+2010000t+88900002010000t8890000)h
Paso 4.1.6
Resta 2010000t2010000t de 2010000t2010000t.
0.000001(131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+0t+8890000-8890000)h0.000001(131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+0t+88900008890000)h
Paso 4.1.7
Resta 88900008890000 de 88900008890000.
0.000001(131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+0t+0)h0.000001(131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+0t+0)h
Paso 4.1.8
Suma 131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+0t131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+0t y 00.
0.000001(131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+0t)h0.000001(131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+0t)h
Paso 4.1.9
Reescribe 131h3+393th2+393t2h+0t3-8500h2-17000th+0t2+2010000h+0t131h3+393th2+393t2h+0t38500h217000th+0t2+2010000h+0t en forma factorizada.
Toca para ver más pasos...
Paso 4.1.9.1
Multiplica 00 por t3t3.
0.000001(131h3+393th2+393t2h+0-8500h2-17000th+0t2+2010000h+0t)h0.000001(131h3+393th2+393t2h+08500h217000th+0t2+2010000h+0t)h
Paso 4.1.9.2
Multiplica 00 por t2t2.
0.000001(131h3+393th2+393t2h+0-8500h2-17000th+0+2010000h+0t)h0.000001(131h3+393th2+393t2h+08500h217000th+0+2010000h+0t)h
Paso 4.1.9.3
Multiplica 00 por tt.
0.000001(131h3+393th2+393t2h+0-8500h2-17000th+0+2010000h+0)h0.000001(131h3+393th2+393t2h+08500h217000th+0+2010000h+0)h
Paso 4.1.9.4
Suma 131h3+393th2+393t2h+0-8500h2-17000th+0+2010000h131h3+393th2+393t2h+08500h217000th+0+2010000h y 00.
0.000001(131h3+393th2+393t2h+0-8500h2-17000th+0+2010000h)h0.000001(131h3+393th2+393t2h+08500h217000th+0+2010000h)h
Paso 4.1.9.5
Suma 131h3131h3 y 00.
0.000001(131h3+393th2+393t2h-8500h2-17000th+0+2010000h)h0.000001(131h3+393th2+393t2h8500h217000th+0+2010000h)h
Paso 4.1.9.6
Suma 131h3131h3 y 00.
0.000001(131h3+393th2+393t2h-8500h2-17000th+2010000h)h0.000001(131h3+393th2+393t2h8500h217000th+2010000h)h
Paso 4.1.9.7
Factoriza hh de 131h3+393th2+393t2h-8500h2-17000th+2010000h131h3+393th2+393t2h8500h217000th+2010000h.
Toca para ver más pasos...
Paso 4.1.9.7.1
Factoriza hh de 131h3131h3.
0.000001(h(131h2)+393th2+393t2h-8500h2-17000th+2010000h)h0.000001(h(131h2)+393th2+393t2h8500h217000th+2010000h)h
Paso 4.1.9.7.2
Factoriza hh de 393th2393th2.
0.000001(h(131h2)+h(393th)+393t2h-8500h2-17000th+2010000h)h0.000001(h(131h2)+h(393th)+393t2h8500h217000th+2010000h)h
Paso 4.1.9.7.3
Factoriza hh de 393t2h393t2h.
0.000001(h(131h2)+h(393th)+h(393t2)-8500h2-17000th+2010000h)h0.000001(h(131h2)+h(393th)+h(393t2)8500h217000th+2010000h)h
Paso 4.1.9.7.4
Factoriza hh de -8500h28500h2.
0.000001(h(131h2)+h(393th)+h(393t2)+h(-8500h)-17000th+2010000h)h0.000001(h(131h2)+h(393th)+h(393t2)+h(8500h)17000th+2010000h)h
Paso 4.1.9.7.5
Factoriza hh de -17000th17000th.
0.000001(h(131h2)+h(393th)+h(393t2)+h(-8500h)+h(-17000t)+2010000h)h0.000001(h(131h2)+h(393th)+h(393t2)+h(8500h)+h(17000t)+2010000h)h
Paso 4.1.9.7.6
Factoriza hh de 2010000h2010000h.
0.000001(h(131h2)+h(393th)+h(393t2)+h(-8500h)+h(-17000t)+h2010000)h0.000001(h(131h2)+h(393th)+h(393t2)+h(8500h)+h(17000t)+h2010000)h
Paso 4.1.9.7.7
Factoriza hh de h(131h2)+h(393th)h(131h2)+h(393th).
0.000001(h(131h2+393th)+h(393t2)+h(-8500h)+h(-17000t)+h2010000)h0.000001(h(131h2+393th)+h(393t2)+h(8500h)+h(17000t)+h2010000)h
Paso 4.1.9.7.8
Factoriza hh de h(131h2+393th)+h(393t2)h(131h2+393th)+h(393t2).
0.000001(h(131h2+393th+393t2)+h(-8500h)+h(-17000t)+h2010000)h0.000001(h(131h2+393th+393t2)+h(8500h)+h(17000t)+h2010000)h
Paso 4.1.9.7.9
Factoriza hh de h(131h2+393th+393t2)+h(-8500h)h(131h2+393th+393t2)+h(8500h).
0.000001(h(131h2+393th+393t2-8500h)+h(-17000t)+h2010000)h0.000001(h(131h2+393th+393t28500h)+h(17000t)+h2010000)h
Paso 4.1.9.7.10
Factoriza hh de h(131h2+393th+393t2-8500h)+h(-17000t)h(131h2+393th+393t28500h)+h(17000t).
0.000001(h(131h2+393th+393t2-8500h-17000t)+h2010000)h0.000001(h(131h2+393th+393t28500h17000t)+h2010000)h
Paso 4.1.9.7.11
Factoriza hh de h(131h2+393th+393t2-8500h-17000t)+h2010000h(131h2+393th+393t28500h17000t)+h2010000.
0.000001(h(131h2+393th+393t2-8500h-17000t+2010000))h0.000001(h(131h2+393th+393t28500h17000t+2010000))h
0.000001(h(131h2+393th+393t2-8500h-17000t+2010000))h0.000001(h(131h2+393th+393t28500h17000t+2010000))h
0.000001h(131h2+393th+393t2-8500h-17000t+2010000)h0.000001h(131h2+393th+393t28500h17000t+2010000)h
0.000001h(131h2+393th+393t2-8500h-17000t+2010000)h0.000001h(131h2+393th+393t28500h17000t+2010000)h
Paso 4.2
Simplifica los términos.
Toca para ver más pasos...
Paso 4.2.1
Cancela el factor común de hh.
Toca para ver más pasos...
Paso 4.2.1.1
Cancela el factor común.
0.000001h(131h2+393th+393t2-8500h-17000t+2010000)h
Paso 4.2.1.2
Divide 0.000001(131h2+393th+393t2-8500h-17000t+2010000) por 1.
0.000001(131h2+393th+393t2-8500h-17000t+2010000)
0.000001(131h2+393th+393t2-8500h-17000t+2010000)
Paso 4.2.2
Aplica la propiedad distributiva.
0.000001(131h2)+0.000001(393th)+0.000001(393t2)+0.000001(-8500h)+0.000001(-17000t)+0.0000012010000
0.000001(131h2)+0.000001(393th)+0.000001(393t2)+0.000001(-8500h)+0.000001(-17000t)+0.0000012010000
Paso 4.3
Simplifica.
Toca para ver más pasos...
Paso 4.3.1
Multiplica 131 por 0.000001.
0.000131h2+0.000001(393th)+0.000001(393t2)+0.000001(-8500h)+0.000001(-17000t)+0.0000012010000
Paso 4.3.2
Multiplica 393 por 0.000001.
0.000131h2+0.000393(th)+0.000001(393t2)+0.000001(-8500h)+0.000001(-17000t)+0.0000012010000
Paso 4.3.3
Multiplica 393 por 0.000001.
0.000131h2+0.000393(th)+0.000393t2+0.000001(-8500h)+0.000001(-17000t)+0.0000012010000
Paso 4.3.4
Multiplica -8500 por 0.000001.
0.000131h2+0.000393(th)+0.000393t2-0.0085h+0.000001(-17000t)+0.0000012010000
Paso 4.3.5
Multiplica -17000 por 0.000001.
0.000131h2+0.000393(th)+0.000393t2-0.0085h-0.017t+0.0000012010000
Paso 4.3.6
Multiplica 0.000001 por 2010000.
0.000131h2+0.000393(th)+0.000393t2-0.0085h-0.017t+2.01
0.000131h2+0.000393(th)+0.000393t2-0.0085h-0.017t+2.01
Paso 4.4
Mueve -0.0085h.
0.000131h2+0.000393th+0.000393t2-0.017t-0.0085h+2.01
Paso 4.5
Mueve 0.000131h2.
0.000393th+0.000393t2+0.000131h2-0.017t-0.0085h+2.01
Paso 4.6
Reordena 0.000393th y 0.000393t2.
0.000393t2+0.000393th+0.000131h2-0.017t-0.0085h+2.01
0.000393t2+0.000393th+0.000131h2-0.017t-0.0085h+2.01
Paso 5
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