Calculus Examples

$lim_{x \to - 3} | x + 3 | - 8 x$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 3$ .

$lim_{x \to - 3} | x + 3 | - lim_{x \to - 3} 8 x$

Step 2

Move the limit inside the absolute value signs.

$| lim_{x \to - 3} x + 3 | - lim_{x \to - 3} 8 x$

Step 3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 3$ .

$| lim_{x \to - 3} x + lim_{x \to - 3} 3 | - lim_{x \to - 3} 8 x$

Step 4

Evaluate the limit of $3$ which is constant as $x$ approaches $- 3$ .

$| lim_{x \to - 3} x + 3 | - lim_{x \to - 3} 8 x$

Step 5

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

$| lim_{x \to - 3} x + 3 | - 8 lim_{x \to - 3} x$

Step 6

Evaluate the limits by plugging in $- 3$ for all occurrences of $x$ .

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Step 6.1

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$| - 3 + 3 | - 8 lim_{x \to - 3} x$

Step 6.2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$| - 3 + 3 | - 8 \cdot - 3$

Step 7

Simplify the answer.

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Step 7.1

Simplify each term.

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Step 7.1.1

Add $- 3$ and $3$ .

$| 0 | - 8 \cdot - 3$

Step 7.1.2

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

$0 - 8 \cdot - 3$

Step 7.1.3

Multiply $- 8$ by $- 3$ .

$0 + 24$

Step 7.2

Add $0$ and $24$ .

$24$