Calculus Examples

$lim_{x \to 4} | 3 x - 5 |$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the absolute value signs.

$| lim_{x \to 4} 3 x - 5 |$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$| lim_{x \to 4} 3 x - lim_{x \to 4} 5 |$

Step 1.3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$| 3 lim_{x \to 4} x - lim_{x \to 4} 5 |$

Step 1.4

Evaluate the limit of $5$ which is constant as $x$ approaches $4$ .

$| 3 lim_{x \to 4} x - 1 \cdot 5 |$

Step 2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$| 3 \cdot 4 - 1 \cdot 5 |$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $3$ by $4$ .

$| 12 - 1 \cdot 5 |$

Step 3.1.2

Multiply $- 1$ by $5$ .

$| 12 - 5 |$

Step 3.2

Subtract $5$ from $12$ .

$| 7 |$

Step 3.3

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$7$