limit as x approaches 2 of (2x-8)/(x-1)

1) Compute the limit of

\frac{2 x - 8}{x - 1}

x \to 2

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

The limit of

2 x

2 \cdot 2

when

x \to 2

⇥1.1) Let's evaluate:

2 \cdot 2

⇥ⅰ

2 \cdot 2

4

⇥

4

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

The limit of

2 x - 8

4 - 8

when

x \to 2

⇥1.2) Let's calculate:

4 - 8

⇥ⓘ Start from

4

and move back

8

on the number line, going below zero:

4 - 8

-4

⇥

-4

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

The limit of

x - 1

2 - 1

when

x \to 2

⇥1.3) Let's evaluate:

2 - 1

⇥ⓘ Start from

2

and move back

1

on the number line:

2 - 1

1

⇥

1

So the limit of

\frac{2 x - 8}{x - 1}

-4

when

x \to 2

▶Limit:

-4