Calculus Examples

$lim_{x \to 4} \frac{4 + 6}{4 (6)}$

Step 1

Cancel the common factor of $4 + 6$ and $4$ .

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Step 1.1

Factor $2$ out of $4$ .

$lim_{x \to 4} \frac{2 (2) + 6}{4 (6)}$

Step 1.2

Factor $2$ out of $6$ .

$lim_{x \to 4} \frac{2 \cdot 2 + 2 \cdot 3}{4 (6)}$

Step 1.3

Factor $2$ out of $2 \cdot 2 + 2 \cdot 3$ .

$lim_{x \to 4} \frac{2 \cdot (2 + 3)}{4 (6)}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $4 (6)$ .

$lim_{x \to 4} \frac{2 \cdot (2 + 3)}{2 (2 \cdot 6)}$

Step 1.4.2

Cancel the common factor.

$lim_{x \to 4} \frac{2 \cdot (2 + 3)}{2 (2 \cdot 6)}$

Step 1.4.3

Rewrite the expression.

$lim_{x \to 4} \frac{2 + 3}{2 \cdot 6}$

Step 2

Evaluate the limit of $\frac{2 + 3}{2 \cdot 6}$ which is constant as $x$ approaches $4$ .

$\frac{2 + 3}{2 \cdot 6}$

Step 3

Simplify the answer.

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Step 3.1

Add $2$ and $3$ .

$\frac{5}{2 \cdot 6}$

Step 3.2

Multiply $2$ by $6$ .

$\frac{5}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$