What is the limit as w approaches-2 of (w^2+5w+6)/(w^3+8) ?

The limit as w approaches-2 of (w^2+5w+6)/(w^3+8) is 1/12

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limit as w approaches-2 of (w^2+5w+6)/(w^3+8)

w \to - 2 lim (\frac{w ^{2} + 5 w + 6}{w ^{3} + 8})

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

w \to - 2 lim (\frac{w ^{2} + 5 w + 6}{w ^{3} + 8})

Simplify

\frac{w ^{2} + 5 w + 6}{w ^{3} + 8} : \frac{w + 3}{w ^{2} - 2 w + 4}

= w \to - 2 lim (\frac{w + 3}{w ^{2} - 2 w + 4})

Plug in the value

w = - 2

= \frac{- 2 + 3}{( - 2 ) ^{2} - 2 ( - 2 ) + 4}

Simplify

\frac{- 2 + 3}{( - 2 ) ^{2} - 2 ( - 2 ) + 4} : \frac{1}{12}

= \frac{1}{12}

\frac{( e ^{2 x} )}{x ^{2} + 1}

\frac{d}{d x} (x^{2} - x + 3)

\frac{\partial}{\partial x} (x^{\frac{3}{4}})

e^{x} - x

2 x

What is the limit as w approaches-2 of (w^2+5w+6)/(w^3+8) ?
The limit as w approaches-2 of (w^2+5w+6)/(w^3+8) is 1/12