limit as x approaches 3 of 3x^4+2x^2-5

1) Let's evaluate the limit of

3 x^{4} + 2 x^{2} - 5

when

x \to 3

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

The limit of

x^{4}

3^{4}

when

x \to 3

⇥1.1) Let's evaluate:

3^{4}

⇥ⓘ An integer power is a repeated product:

3^{4}

3 \cdot 3 \cdot 3 \cdot 3

81

⇥

81

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

The limit of

3 x^{4}

3 \cdot 81

when

x \to 3

⇥1.2) Let's evaluate:

3 \cdot 81

⇥ⅰ

3 \cdot 81

3 \cdot (80 + 1)

3 \cdot 80 + 3

240 + 3

243

⇥

243

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

The limit of

x^{2}

3^{2}

when

x \to 3

⇥1.3) Let's calculate:

3^{2}

⇥ⓘ An integer power is a repeated product:

3^{2}

3 \cdot 3

9

⇥

9

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

The limit of

2 x^{2}

2 \cdot 9

when

x \to 3

⇥1.4) Let's calculate:

2 \cdot 9

⇥ⅰ

2 \cdot 9

18

⇥

18

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

So the limit of

3 x^{4} + 2 x^{2} - 5

243 + 18 - 5

when

x \to 3

⇥1.5) Let's calculate:

243 + 18 - 5

⇥ⓘ Start from

243

and move forward

18

on the number line:

243 + 18

261

⇥

261 - 5

ⓘ Start from

261

and move back

5

on the number line:

261 - 5

256

▶Limit:

256