x³+8 apon x²-4 multiple by x²-6x+8 apon x²-2x+4
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Step-by-step explanation:
Using the formula a³ - b³ = (a-b) (a² + ab + b²) where a = x and b = 2,
x³ - 8 = (x)³ - (2)³ = (x - 2) (x² + 2x + 2²)
Using the formula (a² - b²) = (a + b) (a - b) for a = x and b = 2,
x² - 4 = x² - 2² = (x+2) (x-2)
∴ (x³ - 8) ÷ (x² - 4)
= (x - 2) (x² + 2x + 2²)/(x+2) (x-2)
Cancel x-2 from numerator & denominator, & take limit as x approaches 2. We get
Lim {(x³ - 8) ÷ (x² - 4)} as x → 2
= Lim (x² + 2x + 2²)/(x+2) as x → 2
= (2² + 2 x 2 + 2²)/(2+2)
= (4+4+4)/4 = 3x4/4 = 3 (Proved
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