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

Let's evaluate the limit of

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

when

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

- 2 + 2

when

x \to -2

⇥Let's calculate:

- 2 + 2

⇥ⓘ Start from

-2

and move forward

2

on the number line, up to zero:

- 2 + 2

0

⇥

0

The limit of

- \frac{4}{x + 2}

does not exist when

x \to -2

From the left, the limit is

+∞

; from the right, it is

-∞

. They differ: the limit of

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

does not exist when

x \to -2

▶Limit:

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