limit as x approaches 1+ of 5/(x^3-1)

Compute the limit of

\frac{5}{x^{3} - 1}

x \to 1

⁺

ⓘ The power with a constant exponent is continuous here: substitute the limit of the base

The limit of

x^{3}

1

when

x \to 1

⁺

ⓘ The limit of a sum of finite limits is the sum of the limits

The limit of

x^{3} - 1

is (

1 - 1

)⁺ when

x \to 1

⁺

⇥Let's evaluate:

1 - 1

⇥ⓘ Start from

1

and move back

1

on the number line, down to zero:

1 - 1

0

⇥

0

ⓘ A nonzero number divided by a quantity that tends to 0 grows without bound, the signs giving +∞ or -∞

So the limit of

\frac{5}{x^{3} - 1}

+∞

when

x \to 1

⁺

▶Limit:

+∞