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

The limit as x approaches 2 of (2-x)/(x^3-8) is -1/12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \frac{1}{12}

Decimal

- 0.08333 \dots

Solution steps

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

Simplify

\frac{2 - x}{x ^{3} - 8} : - \frac{1}{x ^{2} + 2 x + 4}

= x \to 2 lim (- \frac{1}{x ^{2} + 2 x + 4})

Plug in the value

x = 2

= - \frac{1}{2 ^{2} + 2 \cdot 2 + 4}

Simplify

= - \frac{1}{12}

x \to - 2 lim ((x + 4) (x - \frac{1}{2}))

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

x \to 0 lim (\frac{0}{sin ^{2} ( x )})

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

x \to 1 - lim (2 - x)

What is the limit as x approaches 2 of (2-x)/(x^3-8) ?
The limit as x approaches 2 of (2-x)/(x^3-8) is -1/12