Calculus Examples

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

Step 1

Move the limit under the radical sign.

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

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

$\sqrt{4 - 4}$

Step 4.2

Simplify the answer.

Tap for more steps...

Step 4.2.1

Subtract $4$ from $4$ .

$\sqrt{0}$

Step 4.2.2

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

$\sqrt{0^{2}}$

Step 4.2.3

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

$0$