Calculus Examples

$lim_{x \to 8} \frac{x}{x - 5}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $8$ .

$\frac{lim_{x \to 8} x}{lim_{x \to 8} x - 5}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$\frac{lim_{x \to 8} x}{lim_{x \to 8} x - lim_{x \to 8} 5}$

Step 3

Evaluate the limit of $5$ which is constant as $x$ approaches $8$ .

$\frac{lim_{x \to 8} x}{lim_{x \to 8} x - 1 \cdot 5}$

Step 4

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{8}{lim_{x \to 8} x - 1 \cdot 5}$

Step 4.2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{8}{8 - 1 \cdot 5}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $- 1$ by $5$ .

$\frac{8}{8 - 5}$

Step 5.2

Subtract $5$ from $8$ .

$\frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$