Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

$\frac{2 ({(lim_{x \to - 4} x)}^{2} - 1 \cdot 16)}{x + 4}$

Step 2

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

$\frac{2 ({(- 4)}^{2} - 1 \cdot 16)}{x + 4}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

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

$\frac{2 (16 - 1 \cdot 16)}{x + 4}$

Step 3.1.2

Multiply $- 1$ by $16$ .

$\frac{2 (16 - 16)}{x + 4}$

Step 3.1.3

Subtract $16$ from $16$ .

$\frac{2 \cdot 0}{x + 4}$

Step 3.2

Multiply $2$ by $0$ .

$\frac{0}{x + 4}$

Step 3.3

Divide $0$ by $x + 4$ .

$0$