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

The limit as x approaches 2 of (8-x^3)/(x^2-2x) is -6

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

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

- 6

Solution steps

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

Simplify

\frac{8 - x ^{3}}{x ^{2} - 2 x} : - \frac{x ^{2} + 2 x + 4}{x}

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

Plug in the value

x = 2

= - \frac{2 ^{2} + 2 \cdot 2 + 4}{2}

Simplify

= - 6

\int \frac{x + x}{x ^{2}} d x

\frac{d}{d x} (7 sin (x) - 7 x cos (x))

\int_{0}^{π} 2 sin (x) d x

\frac{d}{d θ} (- 8 sin (θ))

What is the limit as x approaches 2 of (8-x^3)/(x^2-2x) ?
The limit as x approaches 2 of (8-x^3)/(x^2-2x) is -6