Calculus Examples

$lim_{x \to 0} | f (x) x |$

Step 1

Move the limit inside the absolute value signs.

$| lim_{x \to 0} f (x) x |$

Step 2

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

$| lim_{x \to 0} f (x) \cdot lim_{x \to 0} x |$

Step 3

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

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Step 3.1

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

$| f (0) \cdot lim_{x \to 0} x |$

Step 3.2

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

$| f (0) \cdot 0 |$

Step 4

Simplify the answer.

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Step 4.1

Multiply $f (0)$ by $0$ .

$| 0 |$

Step 4.2

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

$0$