Calculus Examples

$lim_{x \to {(- 4)}^{+}} \sqrt{5 x + 20} - 8$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$lim_{x \to {(- 4)}^{+}} \sqrt{5 x + 20} - lim_{x \to {(- 4)}^{+}} 8$

Step 1.2

Move the limit under the radical sign.

$\sqrt{lim_{x \to {(- 4)}^{+}} 5 x + 20} - lim_{x \to {(- 4)}^{+}} 8$

Step 1.3

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

$\sqrt{lim_{x \to {(- 4)}^{+}} 5 x + lim_{x \to {(- 4)}^{+}} 20} - lim_{x \to {(- 4)}^{+}} 8$

Step 1.4

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{5 lim_{x \to {(- 4)}^{+}} x + lim_{x \to {(- 4)}^{+}} 20} - lim_{x \to {(- 4)}^{+}} 8$

Step 1.5

Evaluate the limit of $20$ which is constant as $x$ approaches $- 4$ .

$\sqrt{5 lim_{x \to {(- 4)}^{+}} x + 20} - lim_{x \to {(- 4)}^{+}} 8$

Step 1.6

Evaluate the limit of $8$ which is constant as $x$ approaches $- 4$ .

$\sqrt{5 lim_{x \to {(- 4)}^{+}} x + 20} - 1 \cdot 8$

Step 2

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

$\sqrt{5 \cdot - 4 + 20} - 1 \cdot 8$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $5$ by $- 4$ .

$\sqrt{- 20 + 20} - 1 \cdot 8$

Step 3.1.2

Add $- 20$ and $20$ .

$\sqrt{0} - 1 \cdot 8$

Step 3.1.3

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

$\sqrt{0^{2}} - 1 \cdot 8$

Step 3.1.4

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

$0 - 1 \cdot 8$

Step 3.1.5

Multiply $- 1$ by $8$ .

$0 - 8$

Step 3.2

Subtract $8$ from $0$ .

$- 8$