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

Let's evaluate the limit of

x^{3}

- 2 x^{2}

+ x

- 3

when

x \to 1

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

The limit of

x^{3}

1

when

x \to 1

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

The limit of

x^{2}

1

when

x \to 1

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

The limit of

- 2 x^{2}

-2

when

x \to 1

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

So the limit of

x^{3}

- 2 x^{2}

+ x

- 3

1

- 2

+ 1

- 3

when

x \to 1

⇥Let's calculate:

1

- 2

+ 1

- 3

⇥ⓘ Start from

1

and move back

2

on the number line, going below zero:

1 - 2

-1

⇥

- 1 + 1 - 3

⇥ⓘ Start from

-1

and move forward

1

on the number line, up to zero:

- 1 + 1

0

⇥

0 - 3

ⓘ Adding 0 changes nothing:

0 - 3

-3

▶Limit:

-3