Calculus Examples

$lim_{x \to 2} x (x - 4)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $2$ .

$lim_{x \to 2} x \cdot lim_{x \to 2} x - 4$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$lim_{x \to 2} x \cdot (lim_{x \to 2} x - lim_{x \to 2} 4)$

Step 3

Evaluate the limit of $4$ which is constant as $x$ approaches $2$ .

$lim_{x \to 2} x \cdot (lim_{x \to 2} x - 1 \cdot 4)$

Step 4

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$2 \cdot (lim_{x \to 2} x - 1 \cdot 4)$

Step 4.2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$2 \cdot (2 - 1 \cdot 4)$

Step 5

Simplify the answer.

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Step 5.1

Multiply $- 1$ by $4$ .

$2 \cdot (2 - 4)$

Step 5.2

Subtract $4$ from $2$ .

$2 \cdot - 2$

Step 5.3

Multiply $2$ by $- 2$ .

$- 4$