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

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

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limit as x approaches 1-of (2x)/(x^3-1)

x \to 1 - lim (\frac{2 x}{x ^{3} - 1})

- \infty

Solution steps

x \to 1 - lim (\frac{2 x}{x ^{3} - 1})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 1 - lim (\frac{x}{x ^{3} - 1})

\frac{x}{x ^{3} - 1} = x \frac{1}{x ^{3} - 1}

= 2 \cdot x \to 1 - lim (x \frac{1}{x ^{3} - 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= 2 \cdot x \to 1 - lim (x) \cdot x \to 1 - lim (\frac{1}{x ^{3} - 1})

x \to 1 - lim (x) = 1

x \to 1 - lim (\frac{1}{x ^{3} - 1}) = - \infty

= 2 \cdot 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{d}{d x} ((x^{4} + 8)^{\frac{1}{2}})

\frac{\partial}{\partial x} (y^{\frac{1}{3}})

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

y = \frac{5}{( 4 x ) ^{- 2}}

\frac{\partial}{\partial x} (sec (y))

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