Calculus Examples

$lim_{x \to 4} \frac{v (3.999) + 2}{(3.999) - 4}$

Step 1

Evaluate the limit of $\frac{v (3.999) + 2}{(3.999) - 4}$ which is constant as $x$ approaches $4$ .

$\frac{v (3.999) + 2}{(3.999) - 4}$

Step 2

Simplify the answer.

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Step 2.1

Subtract $4$ from $3.999$ .

$\frac{v (3.999) + 2}{- 0.001}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{v (3.999) + 2}{0.001}$

Step 2.3

Multiply by $1$ .

$- \frac{1 v (3.999) + 2}{0.001}$

Step 2.4

Rewrite $2$ as $1 (2)$ .

$- \frac{1 v (3.999) + 1 (2)}{0.001}$

Step 2.5

Factor $1$ out of $1 v (3.999) + 1 (2)$ .

$- \frac{1 (v (3.999) + 2)}{0.001}$

Step 2.6

Factor $0.001$ out of $0.001$ .

$- \frac{1 (v (3.999) + 2)}{0.001 (1)}$

Step 2.7

Separate fractions.

$- (\frac{1}{0.001} \cdot \frac{v (3.999) + 2}{1})$

Step 2.8

Divide $1$ by $0.001$ .

$- (1000 \frac{v (3.999) + 2}{1})$

Step 2.9

Divide $v (3.999) + 2$ by $1$ .

$- (1000 (v (3.999) + 2))$

Step 2.10

Apply the distributive property.

$- (1000 v (3.999) + 1000 \cdot 2)$

Step 2.11

Multiply $1000$ by $2$ .

$- (1000 v (3.999) + 2000)$

Step 2.12

Apply the distributive property.

$- (1000 v (3.999)) - 1 \cdot 2000$

Step 2.13

Multiply $1000$ by $- 1$ .

$- 1000 v (3.999) - 1 \cdot 2000$

Step 2.14

Multiply $- 1$ by $2000$ .

$- 1000 v (3.999) - 2000$