limit as x approaches 4 of (2x^3-128)/(sqrt(x)-2)

解答

x \to 4 lim (\frac{2 x ^{3} - 128}{x - 2})

384

求解步骤

x \to 4 lim (\frac{2 x ^{3} - 128}{x - 2})

\frac{2 x ^{3} - 128}{x - 2}

分母有理化:

2 (x^{2} + 4 x + 16) (x + 2)

= x \to 4 lim (2 (x^{2} + 4 x + 16) (x + 2))

代入值

x = 4

= 2 (4^{2} + 4 \cdot 4 + 16) (4 + 2)

化简

2 (4^{2} + 4 \cdot 4 + 16) (4 + 2) : 384

= 384

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