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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Simplify

\frac{x - 1}{x ^{3} - 1} : \frac{1}{x ^{2} + x + 1}

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

Plug in the value

x = 1

= \frac{1}{1 ^{2} + 1 + 1}

Simplify

= \frac{1}{3}

y^{^{''}} - 4 y^{^{'}} - 12 y = 0

2 y

\frac{d y}{d x}, y = arccos (4 x^{2})

\int 3 sin (2 x) cos (3 x) d x

\int_{0}^{4} ((4 - x) x) d x

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