limit as x approaches 2 of x^3-5x — step-by-step solution

Let's evaluate the limit of

x^{3} - 5 x

when

x \to 2

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

The limit of

x^{3}

2^{3}

when

x \to 2

⇥Let's evaluate:

2^{3}

⇥ⓘ An integer power is a repeated product:

2^{3}

2 \cdot 2 \cdot 2

8

⇥

8

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

The limit of

- 5 x

- 5 \cdot 2

when

x \to 2

⇥Let's evaluate:

- 5 \cdot 2

⇥ⓘ A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

- 5 \cdot 2

-10

⇥

-10

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

So the limit of

x^{3} - 5 x

8 - 10

when

x \to 2

⇥Let's evaluate:

8 - 10

ⓘ Start from

8

and move back

10

on the number line, going below zero:

8 - 10

-2

▶Limit:

-2