Calculus Examples

$\frac{lim_{x \to 16} x - 16}{x^{2} - 256}$

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 $16$ .

$\frac{lim_{x \to 16} x - lim_{x \to 16} 16}{x^{2} - 256}$

Step 1.2

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

$\frac{lim_{x \to 16} x - 1 \cdot 16}{x^{2} - 256}$

Step 2

Evaluate the limit of $x$ by plugging in $16$ for $x$ .

$\frac{16 - 1 \cdot 16}{x^{2} - 256}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Multiply $- 1$ by $16$ .

$\frac{16 - 16}{x^{2} - 256}$

Step 3.1.2

Subtract $16$ from $16$ .

$\frac{0}{x^{2} - 256}$

Step 3.2

Simplify the denominator.

Tap for more steps...

Step 3.2.1

Rewrite $256$ as $16^{2}$ .

$\frac{0}{x^{2} - 16^{2}}$

Step 3.2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 16$ .

$\frac{0}{(x + 16) (x - 16)}$

Step 3.3

Divide $0$ by $(x + 16) (x - 16)$ .

$0$