limit as x approaches -6+ of (-2x)/(x+6)

Compute the limit of

- \frac{2 x}{x + 6}

x \to -6

⁺

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

The limit of

- 2 x

- 2 \cdot (-6)

when

x \to -6

⁺

⇥Let's evaluate:

- 2 \cdot (-6)

⇥ⓘ Two minus signs cancel out, the product of two negative numbers is positive:

- 2 \cdot (-6)

12

⇥

12

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

The limit of

x + 6

is (

- 6 + 6

)⁺ when

x \to -6

⁺

⇥Let's evaluate:

- 6 + 6

⇥ⓘ Start from

-6

and move forward

6

on the number line, up to zero:

- 6 + 6

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{2 x}{x + 6}

+∞

when

x \to -6

⁺

▶Limit:

+∞