Calculus Examples

$lim_{x \to 7} \frac{f (8) + g (8)}{6 g (8)}$

Step 1

Evaluate the limit of $\frac{f (8) + g (8)}{6 g (8)}$ which is constant as $x$ approaches $7$ .

$\frac{f (8) + g (8)}{6 g (8)}$

Step 2

Simplify the answer.

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Step 2.1

Add $f (8)$ and $g (8)$ .

$\frac{2 f (8)}{6 g (8)}$

Step 2.2

Cancel the common factor of $2$ and $6$ .

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Step 2.2.1

Factor $2$ out of $2 f (8)$ .

$\frac{2 (f (8))}{6 g (8)}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $6 g (8)$ .

$\frac{2 (f (8))}{2 (3 g (8))}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 f (8)}{2 (3 g (8))}$

Step 2.2.2.3

Rewrite the expression.

$\frac{f (8)}{3 g (8)}$

Step 2.3

Cancel the common factor of $f (8)$ and $g (8)$ .

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Step 2.3.1

Cancel the common factor.

$\frac{f (8)}{3 g (8)}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$