Calculus Examples

$\frac{lim_{x \to 8} 8 x - 5}{7 x + 4}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{x \to 8} 8 x - lim_{x \to 8} 5}{7 x + 4}$

Step 1.2

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$\frac{8 lim_{x \to 8} x - lim_{x \to 8} 5}{7 x + 4}$

Step 1.3

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

$\frac{8 lim_{x \to 8} x - 1 \cdot 5}{7 x + 4}$

Step 2

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

$\frac{8 \cdot 8 - 1 \cdot 5}{7 x + 4}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $8$ by $8$ .

$\frac{64 - 1 \cdot 5}{7 x + 4}$

Step 3.2

Multiply $- 1$ by $5$ .

$\frac{64 - 5}{7 x + 4}$

Step 3.3

Subtract $5$ from $64$ .

$\frac{59}{7 x + 4}$