Calculus Examples

$lim_{x \to 4^{-}} \sqrt{16 - x^{2}}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 4^{-}} 16 - x^{2}}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$\sqrt{lim_{x \to 4^{-}} 16 - lim_{x \to 4^{-}} x^{2}}$

Step 1.3

Evaluate the limit of $16$ which is constant as $x$ approaches $4$ .

$\sqrt{16 - lim_{x \to 4^{-}} x^{2}}$

Step 1.4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\sqrt{16 - {(lim_{x \to 4^{-}} x)}^{2}}$

Step 2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\sqrt{16 - 4^{2}}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Raise $4$ to the power of $2$ .

$\sqrt{16 - 1 \cdot 16}$

Step 3.2

Multiply $- 1$ by $16$ .

$\sqrt{16 - 16}$

Step 3.3

Subtract $16$ from $16$ .

$\sqrt{0}$

Step 3.4

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}}$

Step 3.5

Pull terms out from under the radical, assuming positive real numbers.

$0$