What is the limit as x approaches 8 of (3x^2-24x)/(x^2-64) ?

The limit as x approaches 8 of (3x^2-24x)/(x^2-64) is 3/2

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limit as x approaches 8 of (3x^2-24x)/(x^2-64)

x \to 8 lim (\frac{3 x ^{2} - 24 x}{x ^{2} - 64})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 8 lim (\frac{3 x ^{2} - 24 x}{x ^{2} - 64})

Simplify

\frac{3 x ^{2} - 24 x}{x ^{2} - 64} : \frac{3 x}{x + 8}

= x \to 8 lim (\frac{3 x}{x + 8})

Plug in the value

x = 8

= \frac{3 \cdot 8}{8 + 8}

Simplify

\frac{3 \cdot 8}{8 + 8} : \frac{3}{2}

= \frac{3}{2}

What is the limit as x approaches 8 of (3x^2-24x)/(x^2-64) ?
The limit as x approaches 8 of (3x^2-24x)/(x^2-64) is 3/2