Calculus Examples

$\frac{lim_{x \to 8} 5 x - 1}{2 x + 5}$

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 $8$ .

$\frac{lim_{x \to 8} 5 x - lim_{x \to 8} 1}{2 x + 5}$

Step 1.2

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\frac{5 lim_{x \to 8} x - lim_{x \to 8} 1}{2 x + 5}$

Step 1.3

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

$\frac{5 lim_{x \to 8} x - 1 \cdot 1}{2 x + 5}$

Step 2

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

$\frac{5 \cdot 8 - 1 \cdot 1}{2 x + 5}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $5$ by $8$ .

$\frac{40 - 1 \cdot 1}{2 x + 5}$

Step 3.2

Multiply $- 1$ by $1$ .

$\frac{40 - 1}{2 x + 5}$

Step 3.3

Subtract $1$ from $40$ .

$\frac{39}{2 x + 5}$