limit as x approaches 6 of x^2-36 — step-by-step solution

Let's evaluate the limit of

x^{2} - 36

when

x \to 6

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

The limit of

x^{2}

6^{2}

when

x \to 6

⇥Let's calculate:

6^{2}

⇥ⓘ An integer power is a repeated product:

6^{2}

6 \cdot 6

36

⇥

36

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

So the limit of

x^{2} - 36

36 - 36

when

x \to 6

⇥Let's calculate:

36 - 36

ⓘ Start from

36

and move back

36

on the number line, down to zero:

36 - 36

0

▶Limit:

0