Math, asked by vedaanshtyagi956, 8 months ago

limx-2( x³-8)/(x²-4)​

Answers

Answered by adityarawat27
7

Answer:

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)

Step-by-step explanation:

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Answered by baljitkumar401866
2

Answer:

lim Xtends2 x³-8/x²-4

lim Xtends2. x³-2³/x²-2²

limXtends2. x³-2³/(x-2) (x+2)

using the formula. (lim Xtendsa xⁿ-aⁿ/x-a = naⁿ-¹)

3(2)²*lim Xtends2 1/x+2

12 Lim Xtends2 1/x+2

12/4 = 3

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