limit as x approaches -2- of x/(x^2-4)

Compute the limit of

\frac{x}{x^{2} - 4}

x \to -2

⁻

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

The limit of

x^{2}

{(-2)}^{2}

when

x \to -2

⁻

⇥Let's calculate:

{(-2)}^{2}

⇥ⓘ An integer power is a repeated product. The minus signs cancel out in pairs, an even power of a negative number is positive:

{(-2)}^{2}

(-2) \cdot (-2)

4

⇥

4

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

The limit of

x^{2} - 4

is (

4 - 4

)⁺ when

x \to -2

⁻

⇥Let's calculate:

4 - 4

⇥ⓘ Start from

4

and move back

4

on the number line, down to zero:

4 - 4

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{x}{x^{2} - 4}

-∞

when

x \to -2

⁻

▶Limit:

-∞