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

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

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

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

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

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

Simplify

\frac{x - 2}{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}

f^{^{'}} (x) = x^{3} - 5 x^{2} + 3

256 = 4 x^{2} + 2 x y - 4 y^{3}, (2, - 4)

\int \frac{cos ( 3 x )}{sin ( 3 x )} d x

\int \frac{cos ( 2 x )}{cos ^{2} ( x ) sin ^{2} ( x )} d x

\int \frac{1}{( u ^{2} + a ^{2} ) ^{2}} d u

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