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

The limit as x approaches 2 of 1/(x(x^2-2)) is 1/4

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limit as x approaches 2 of 1/(x(x^2-2))

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Plug in the value

x = 2

= \frac{1}{2 ( 2 ^{2} - 2 )}

Simplify

= \frac{1}{4}

\frac{d y}{d x} = \frac{2 x y}{x ^{2} - y ^{2}}, y (1) = 1

\frac{6}{( s ^{3} - 2 ) ^{3}}

\frac{\partial}{\partial y} (x - \frac{1}{y ^{2}})

y = - x^{2} + 4, y = - \frac{x ^{2}}{2} + 2

\frac{1}{( s ^{2} + s + 1 )}

What is the limit as x approaches 2 of 1/(x(x^2-2)) ?
The limit as x approaches 2 of 1/(x(x^2-2)) is 1/4