Respuesta:
Explicación paso a paso:
factorizacion del numerador
x⁴ - 1 = (x²)² - 1
= (x² - 1).(x² + 1)
= (x - 1).(x + 1).(x² + 1)
factorizacion de divisor
x³ - x² + x - 1 = (x³ - x²) + (x - 1)
= x²(x - 1) + (x - 1)
= (x - 1).(x² + 1)
entonces
lim x→1 (x⁴ - 1)/(x³ - x² + x - 1)
lim x→1 (x - 1).(x + 1).(x² + 1)/(x - 1).(x² + 1)
lim x→1 (x + 1)
se toma limite
lim x→1 (x + 1) = 1 + 1 = 2
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Respuesta:
lim x→1 (x⁴ - 1)/(x³ - x² + x - 1)= 2
Explicación paso a paso:
factorizacion del numerador
x⁴ - 1 = (x²)² - 1
= (x² - 1).(x² + 1)
= (x - 1).(x + 1).(x² + 1)
factorizacion de divisor
x³ - x² + x - 1 = (x³ - x²) + (x - 1)
= x²(x - 1) + (x - 1)
= (x - 1).(x² + 1)
entonces
lim x→1 (x⁴ - 1)/(x³ - x² + x - 1)
lim x→1 (x - 1).(x + 1).(x² + 1)/(x - 1).(x² + 1)
lim x→1 (x + 1)
se toma limite
lim x→1 (x + 1) = 1 + 1 = 2