Calculus Examples

$lim_{x \to 0} | \frac{x}{x + 1} |$

Step 1

Move the limit inside the absolute value signs.

$| lim_{x \to 0} \frac{x}{x + 1} |$

Step 2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0$ .

$| \frac{lim_{x \to 0} x}{lim_{x \to 0} x + 1} |$

Step 3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$| \frac{lim_{x \to 0} x}{lim_{x \to 0} x + lim_{x \to 0} 1} |$

Step 4

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$| \frac{lim_{x \to 0} x}{lim_{x \to 0} x + 1} |$

Step 5

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$| \frac{0}{lim_{x \to 0} x + 1} |$

Step 5.2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$| \frac{0}{0 + 1} |$

Step 6

Simplify the answer.

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Step 6.1

Add $0$ and $1$ .

$| \frac{0}{1} |$

Step 6.2

Divide $0$ by $1$ .

$| 0 |$

Step 6.3

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

$0$