limit as x approaches 3- of ln(x^2-9)

Compute the limit of

\ln (x^{2} - 9)

x \to 3

⁻

ⓘ 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

⁻

⇥Let's evaluate:

3^{2}

⇥ⓘ An integer power is a repeated product:

3^{2}

3 \cdot 3

9

⇥

9

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

The limit of

x^{2} - 9

is (

9 - 9

)⁻ when

x \to 3

⁻

⇥Let's evaluate:

9 - 9

⇥ⓘ Start from

9

and move back

9

on the number line, down to zero:

9 - 9

0

⇥

0

So the limit of

\ln (x^{2} - 9)

does not exist when

x \to 3

⁻

▶Limit:

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