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

Compute the limit of

\sqrt{9 - x^{2}}

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}

⇥ⓘ Without parentheses, the minus sign is not part of the power■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

9 - x^{2}

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

ⓘ The function sqrt is continuous, its limit is its value at the limit of its argument

So the limit of

\sqrt{9 - x^{2}}

\sqrt{0}

⁺ when

x \to 3

⁻

⇥Let's calculate:

\sqrt{0}

▶Limit:

0