Calculus Examples

$\frac{lim_{x \to - 7} 7 - | x |}{7 + x}$

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 $- 7$ .

$\frac{lim_{x \to - 7} 7 - lim_{x \to - 7} | x |}{7 + x}$

Step 1.2

Evaluate the limit of $7$ which is constant as $x$ approaches $- 7$ .

$\frac{7 - lim_{x \to - 7} | x |}{7 + x}$

Step 1.3

Move the limit inside the absolute value signs.

$\frac{7 - | lim_{x \to - 7} x |}{7 + x}$

Step 2

Evaluate the limit of $x$ by plugging in $- 7$ for $x$ .

$\frac{7 - | - 7 |}{7 + x}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$\frac{7 - 1 \cdot 7}{7 + x}$

Step 3.1.2

Multiply $- 1$ by $7$ .

$\frac{7 - 7}{7 + x}$

Step 3.1.3

Subtract $7$ from $7$ .

$\frac{0}{7 + x}$

Step 3.2

Divide $0$ by $7 + x$ .

$0$