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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Simplify

\frac{x + 1}{x ^{3} - x} : \frac{1}{x ( x - 1 )}

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

Plug in the value

x = - 1

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

Simplify

= \frac{1}{2}

a \to 0 lim (cot (a) - csc (a))

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

x \to 0 + lim (x^{2 x + 1})

x \to 2 + lim (\frac{∣ x - 2 ∣}{2 - x})

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

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