limit as x approaches 2 of 3x^2-2x+1

1) Compute the limit of

3 x^{2} - 2 x + 1

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

⇥1.1) Let's calculate:

2^{2}

⇥ⓘ An integer power is a repeated product:

2^{2}

2 \cdot 2

4

⇥

4

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

The limit of

3 x^{2}

3 \cdot 4

when

x \to 2

⇥1.2) Let's evaluate:

3 \cdot 4

⇥ⅰ

3 \cdot 4

12

⇥

12

ⓘ 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

⇥1.3) Let's evaluate:

- 2 \cdot 2

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

- 2 \cdot 2

-4

⇥

-4

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

So the limit of

3 x^{2} - 2 x + 1

12 - 4 + 1

when

x \to 2

⇥1.4) Let's evaluate:

12 - 4 + 1

⇥ⓘ Start from

12

and move back

4

on the number line:

12 - 4

8

⇥

8 + 1

ⓘ Start from

8

and move forward

1

on the number line:

8 + 1

9

▶Limit:

9