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

The limit as x approaches 3+of x/(3x-x^3) is -1/6

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limit as x approaches 3+of x/(3x-x^3)

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

- \frac{1}{6}

Decimal Notation

- 0.16666 \dots

Solution steps

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

Plug in the value

x = 3

= \frac{3}{3 \cdot 3 - 3 ^{3}}

Simplify

\frac{3}{3 \cdot 3 - 3 ^{3}} : - \frac{1}{6}

= - \frac{1}{6}

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

x \to 0 lim ((cos (x))^{c o t^{2} (x)})

ln (\frac{( 1 + x )}{( 1 - x )})

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

\frac{1}{x ^{9}}

What is the limit as x approaches 3+of x/(3x-x^3) ?
The limit as x approaches 3+of x/(3x-x^3) is -1/6