What is the limit as x approaches 0 of (x^3-8x)/(x^2+4x) ?

The limit as x approaches 0 of (x^3-8x)/(x^2+4x) is -2

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limit as x approaches 0 of (x^3-8x)/(x^2+4x)

x \to 0 lim (\frac{x ^{3} - 8 x}{x ^{2} + 4 x})

- 2

Solution steps

x \to 0 lim (\frac{x ^{3} - 8 x}{x ^{2} + 4 x})

Simplify

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

= x \to 0 lim (\frac{x ^{2} - 8}{x + 4})

Plug in the value

x = 0

= \frac{0 ^{2} - 8}{0 + 4}

Simplify

\frac{0 ^{2} - 8}{0 + 4} : - 2

= - 2

x \to 2 lim (7 x)

x \to 4 lim (\frac{0}{0})

x \to - 5 lim (\frac{x + 5}{∣ x + 5 ∣})

x \to 2 lim (6 x)

x \to π lim ((x - π) (cot (x)))

What is the limit as x approaches 0 of (x^3-8x)/(x^2+4x) ?
The limit as x approaches 0 of (x^3-8x)/(x^2+4x) is -2