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

Let's evaluate the limit of

- \frac{1}{x^{2} - 1}

when

x \to 1

⁻

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

The limit of

x^{2}

1

when

x \to 1

⁻

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

The limit of

x^{2} - 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{1}{x^{2} - 1}

+∞

when

x \to 1

⁻

▶Limit:

+∞