Calculus Examples

$\frac{lim_{x \to 16} v x - 16}{x - 16}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $16$ .

$\frac{lim_{x \to 16} v x - lim_{x \to 16} 16}{x - 16}$

Step 1.2

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

$\frac{v lim_{x \to 16} x - lim_{x \to 16} 16}{x - 16}$

Step 1.3

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

$\frac{v lim_{x \to 16} x - 1 \cdot 16}{x - 16}$

Step 2

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

$\frac{v \cdot 16 - 1 \cdot 16}{x - 16}$

Step 3

Simplify the numerator.

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Step 3.1

Move $16$ to the left of $v$ .

$\frac{16 \cdot v - 1 \cdot 16}{x - 16}$

Step 3.2

Multiply $- 1$ by $16$ .

$\frac{16 v - 16}{x - 16}$

Step 3.3

Factor $16$ out of $16 v - 16$ .

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Step 3.3.1

Factor $16$ out of $16 v$ .

$\frac{16 (v) - 16}{x - 16}$

Step 3.3.2

Factor $16$ out of $- 16$ .

$\frac{16 (v) + 16 (- 1)}{x - 16}$

Step 3.3.3

Factor $16$ out of $16 (v) + 16 (- 1)$ .

$\frac{16 (v - 1)}{x - 16}$