Calculus Examples

$lim_{x \to - 8} \frac{x}{4 x - 1}$

Step 1

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

$\frac{lim_{x \to - 8} x}{lim_{x \to - 8} 4 x - 1}$

Step 2

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

$\frac{lim_{x \to - 8} x}{lim_{x \to - 8} 4 x - lim_{x \to - 8} 1}$

Step 3

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$\frac{lim_{x \to - 8} x}{4 lim_{x \to - 8} x - lim_{x \to - 8} 1}$

Step 4

Evaluate the limit of $1$ which is constant as $x$ approaches $- 8$ .

$\frac{lim_{x \to - 8} x}{4 lim_{x \to - 8} x - 1 \cdot 1}$

Step 5

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

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Step 5.1

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

$\frac{- 8}{4 lim_{x \to - 8} x - 1 \cdot 1}$

Step 5.2

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

$\frac{- 8}{4 \cdot - 8 - 1 \cdot 1}$

Step 6

Simplify the answer.

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Step 6.1

Simplify the denominator.

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Step 6.1.1

Multiply $4$ by $- 8$ .

$\frac{- 8}{- 32 - 1 \cdot 1}$

Step 6.1.2

Multiply $- 1$ by $1$ .

$\frac{- 8}{- 32 - 1}$

Step 6.1.3

Subtract $1$ from $- 32$ .

$\frac{- 8}{- 33}$

Step 6.2

Dividing two negative values results in a positive value.

$\frac{8}{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{33}$

Decimal Form:

$0.\overline{24}$