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Precálculo Ejemplos
C(x)=1.74x2C(x)=1.74x2
Paso 1
Considera la fórmula del cociente diferencial.
f(x+h)-f(x)hf(x+h)−f(x)h
Paso 2
Paso 2.1
Evalúa la función en x=x+hx=x+h.
Paso 2.1.1
Reemplaza la variable xx con x+hx+h en la expresión.
C(x+h)=1.74(x+h)2C(x+h)=1.74(x+h)2
Paso 2.1.2
Simplifica el resultado.
Paso 2.1.2.1
Reescribe (x+h)2(x+h)2 como (x+h)(x+h)(x+h)(x+h).
C(x+h)=1.74((x+h)(x+h))C(x+h)=1.74((x+h)(x+h))
Paso 2.1.2.2
Expande (x+h)(x+h)(x+h)(x+h) con el método PEIU (primero, exterior, interior, ultimo).
Paso 2.1.2.2.1
Aplica la propiedad distributiva.
C(x+h)=1.74(x(x+h)+h(x+h))C(x+h)=1.74(x(x+h)+h(x+h))
Paso 2.1.2.2.2
Aplica la propiedad distributiva.
C(x+h)=1.74(x⋅x+xh+h(x+h))C(x+h)=1.74(x⋅x+xh+h(x+h))
Paso 2.1.2.2.3
Aplica la propiedad distributiva.
C(x+h)=1.74(x⋅x+xh+hx+h⋅h)C(x+h)=1.74(x⋅x+xh+hx+h⋅h)
C(x+h)=1.74(x⋅x+xh+hx+h⋅h)C(x+h)=1.74(x⋅x+xh+hx+h⋅h)
Paso 2.1.2.3
Simplifica y combina los términos similares.
Paso 2.1.2.3.1
Simplifica cada término.
Paso 2.1.2.3.1.1
Multiplica xx por xx.
C(x+h)=1.74(x2+xh+hx+h⋅h)C(x+h)=1.74(x2+xh+hx+h⋅h)
Paso 2.1.2.3.1.2
Multiplica hh por hh.
C(x+h)=1.74(x2+xh+hx+h2)C(x+h)=1.74(x2+xh+hx+h2)
C(x+h)=1.74(x2+xh+hx+h2)C(x+h)=1.74(x2+xh+hx+h2)
Paso 2.1.2.3.2
Suma xhxh y hxhx.
Paso 2.1.2.3.2.1
Reordena xx y hh.
C(x+h)=1.74(x2+hx+hx+h2)C(x+h)=1.74(x2+hx+hx+h2)
Paso 2.1.2.3.2.2
Suma hxhx y hxhx.
C(x+h)=1.74(x2+2hx+h2)C(x+h)=1.74(x2+2hx+h2)
C(x+h)=1.74(x2+2hx+h2)C(x+h)=1.74(x2+2hx+h2)
C(x+h)=1.74(x2+2hx+h2)C(x+h)=1.74(x2+2hx+h2)
Paso 2.1.2.4
Aplica la propiedad distributiva.
C(x+h)=1.74x2+1.74(2hx)+1.74h2C(x+h)=1.74x2+1.74(2hx)+1.74h2
Paso 2.1.2.5
Multiplica 22 por 1.741.74.
C(x+h)=1.74x2+3.48hx+1.74h2C(x+h)=1.74x2+3.48hx+1.74h2
Paso 2.1.2.6
La respuesta final es 1.74x2+3.48hx+1.74h21.74x2+3.48hx+1.74h2.
1.74x2+3.48hx+1.74h21.74x2+3.48hx+1.74h2
1.74x2+3.48hx+1.74h21.74x2+3.48hx+1.74h2
1.74x2+3.48hx+1.74h21.74x2+3.48hx+1.74h2
Paso 2.2
Reordena.
Paso 2.2.1
Mueve 1.74x21.74x2.
3.48hx+1.74h2+1.74x23.48hx+1.74h2+1.74x2
Paso 2.2.2
Reordena 3.48hx3.48hx y 1.74h21.74h2.
1.74h2+3.48hx+1.74x21.74h2+3.48hx+1.74x2
1.74h2+3.48hx+1.74x21.74h2+3.48hx+1.74x2
Paso 2.3
Obtén los componentes de la definición.
C(x+h)=1.74h2+3.48hx+1.74x2C(x+h)=1.74h2+3.48hx+1.74x2
C(x)=1.74x2C(x)=1.74x2
C(x+h)=1.74h2+3.48hx+1.74x2C(x+h)=1.74h2+3.48hx+1.74x2
C(x)=1.74x2C(x)=1.74x2
Paso 3
Inserta los componentes.
C(x+h)-Cxh=1.74h2+3.48hx+1.74x2-(1.74x2)hC(x+h)−Cxh=1.74h2+3.48hx+1.74x2−(1.74x2)h
Paso 4
Paso 4.1
Simplifica el numerador.
Paso 4.1.1
Factoriza 0.020.02 de 1.74h2+3.48hx+1.74x2-1⋅1.74x21.74h2+3.48hx+1.74x2−1⋅1.74x2.
Paso 4.1.1.1
Mueve hh.
1.74h2+3.48xh+1.74x2-1⋅1.74x2h1.74h2+3.48xh+1.74x2−1⋅1.74x2h
Paso 4.1.1.2
Factoriza 0.020.02 de 1.74h21.74h2.
0.02(87h2)+3.48xh+1.74x2-1⋅1.74x2h0.02(87h2)+3.48xh+1.74x2−1⋅1.74x2h
Paso 4.1.1.3
Factoriza 0.020.02 de 3.48xh3.48xh.
0.02(87h2)+0.02(174xh)+1.74x2-1⋅1.74x2h0.02(87h2)+0.02(174xh)+1.74x2−1⋅1.74x2h
Paso 4.1.1.4
Factoriza 0.020.02 de 1.74x21.74x2.
0.02(87h2)+0.02(174xh)+0.02(87x2)-1⋅1.74x2h0.02(87h2)+0.02(174xh)+0.02(87x2)−1⋅1.74x2h
Paso 4.1.1.5
Factoriza 0.020.02 de -1⋅1.74x2−1⋅1.74x2.
0.02(87h2)+0.02(174xh)+0.02(87x2)+0.02(-50⋅1.74x2)h0.02(87h2)+0.02(174xh)+0.02(87x2)+0.02(−50⋅1.74x2)h
Paso 4.1.1.6
Factoriza 0.020.02 de 0.02(87h2)+0.02(174xh)0.02(87h2)+0.02(174xh).
0.02(87h2+174xh)+0.02(87x2)+0.02(-50⋅1.74x2)h0.02(87h2+174xh)+0.02(87x2)+0.02(−50⋅1.74x2)h
Paso 4.1.1.7
Factoriza 0.020.02 de 0.02(87h2+174xh)+0.02(87x2)0.02(87h2+174xh)+0.02(87x2).
0.02(87h2+174xh+87x2)+0.02(-50⋅1.74x2)h0.02(87h2+174xh+87x2)+0.02(−50⋅1.74x2)h
Paso 4.1.1.8
Factoriza 0.020.02 de 0.02(87h2+174xh+87x2)+0.02(-50⋅1.74x2)0.02(87h2+174xh+87x2)+0.02(−50⋅1.74x2).
0.02(87h2+174xh+87x2-50⋅1.74x2)h0.02(87h2+174xh+87x2−50⋅1.74x2)h
0.02(87h2+174xh+87x2-50⋅1.74x2)h0.02(87h2+174xh+87x2−50⋅1.74x2)h
Paso 4.1.2
Multiplica -50−50 por 1.741.74.
0.02(87h2+174xh+87x2-87x2)h0.02(87h2+174xh+87x2−87x2)h
Paso 4.1.3
Resta 87x287x2 de 87x287x2.
0.02(87h2+174xh+0x2)h0.02(87h2+174xh+0x2)h
Paso 4.1.4
Reescribe 87h2+174xh+0x287h2+174xh+0x2 en forma factorizada.
Paso 4.1.4.1
Factoriza 8787 de 87h2+174xh+0x287h2+174xh+0x2.
Paso 4.1.4.1.1
Factoriza 8787 de 87h287h2.
0.02(87h2+174xh+0x2)h0.02(87h2+174xh+0x2)h
Paso 4.1.4.1.2
Factoriza 8787 de 174xh174xh.
0.02(87h2+87(2xh)+0x2)h0.02(87h2+87(2xh)+0x2)h
Paso 4.1.4.1.3
Factoriza 8787 de 0x20x2.
0.02(87h2+87(2xh)+87(0x2))h0.02(87h2+87(2xh)+87(0x2))h
Paso 4.1.4.1.4
Factoriza 8787 de 87h2+87(2xh)87h2+87(2xh).
0.02(87(h2+2xh)+87(0x2))h0.02(87(h2+2xh)+87(0x2))h
Paso 4.1.4.1.5
Factoriza 8787 de 87(h2+2xh)+87(0x2)87(h2+2xh)+87(0x2).
0.02(87(h2+2xh+0x2))h0.02(87(h2+2xh+0x2))h
0.02(87(h2+2xh+0x2))h0.02(87(h2+2xh+0x2))h
Paso 4.1.4.2
Multiplica 00 por x2x2.
0.02(87(h2+2xh+0))h0.02(87(h2+2xh+0))h
Paso 4.1.4.3
Suma h2+2xh y 0.
0.02(87(h2+2xh))h
Paso 4.1.4.4
Factoriza h de h2+2xh.
Paso 4.1.4.4.1
Factoriza h de h2.
0.02(87(h⋅h+2xh))h
Paso 4.1.4.4.2
Factoriza h de 2xh.
0.02(87(h(h)+h(2x)))h
Paso 4.1.4.4.3
Factoriza h de h(h)+h(2x).
0.02(87(h(h+2x)))h
0.02(87h(h+2x))h
0.02⋅87h(h+2x)h
Paso 4.1.5
Multiplica 0.02 por 87.
1.74h(h+2x)h
1.74h(h+2x)h
Paso 4.2
Simplifica los términos.
Paso 4.2.1
Cancela el factor común de h.
Paso 4.2.1.1
Cancela el factor común.
1.74h(h+2x)h
Paso 4.2.1.2
Divide 1.74(h+2x) por 1.
1.74(h+2x)
1.74(h+2x)
Paso 4.2.2
Aplica la propiedad distributiva.
1.74h+1.74(2x)
Paso 4.2.3
Simplifica la expresión.
Paso 4.2.3.1
Multiplica 2 por 1.74.
1.74h+3.48x
Paso 4.2.3.2
Reordena 1.74h y 3.48x.
3.48x+1.74h
3.48x+1.74h
3.48x+1.74h
3.48x+1.74h
Paso 5