What is the limit as x approaches 4 of (2x^3-128)/(sqrt(x)-2) ?

The limit as x approaches 4 of (2x^3-128)/(sqrt(x)-2) is 384

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

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

384

Solution steps

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

Rationalize denominator

\frac{2 x ^{3} - 128}{x - 2} : 2 (x^{2} + 4 x + 16) (x + 2)

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

Plug in the value

x = 4

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

Simplify

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

= 384

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x + \frac{7}{x}

\int \frac{ln ( 3 x )}{x ^{2}} d x

\frac{d}{d x} (2 e^{2 x - 1})

\int_{- 2}^{3} \frac{44}{x ^{4}} d x

What is the limit as x approaches 4 of (2x^3-128)/(sqrt(x)-2) ?
The limit as x approaches 4 of (2x^3-128)/(sqrt(x)-2) is 384