limit as x approaches -1 of 3x^4-6x+1

1) Compute the limit of

3 x^{4} - 6 x + 1

x \to -1

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

The limit of

x^{4}

{(-1)}^{4}

when

x \to -1

⇥1.1) Let's evaluate:

{(-1)}^{4}

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

{(-1)}^{4}

(-1) \cdot (-1) \cdot (-1) \cdot (-1)

1

⇥

1

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

The limit of

3 x^{4}

3

when

x \to -1

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

The limit of

- 6 x

- 6 \cdot (-1)

when

x \to -1

⇥1.2) Let's evaluate:

- 6 \cdot (-1)

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

- 6 \cdot (-1)

6

⇥

6

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

So the limit of

3 x^{4} - 6 x + 1

3 + 6 + 1

when

x \to -1

⇥1.3) Let's calculate:

3 + 6 + 1

⇥ⓘ Start from

3

and move forward

6

on the number line:

3 + 6

9

⇥

9 + 1

ⓘ Start from

9

and move forward

1

on the number line:

9 + 1

10

▶Limit:

10