Calculus Examples

$lim_{x \to 4} x (x - 3)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} x \cdot lim_{x \to 4} x - 3$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} x \cdot (lim_{x \to 4} x - lim_{x \to 4} 3)$

Step 3

Evaluate the limit of $3$ which is constant as $x$ approaches $4$ .

$lim_{x \to 4} x \cdot (lim_{x \to 4} x - 1 \cdot 3)$

Step 4

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 \cdot (lim_{x \to 4} x - 1 \cdot 3)$

Step 4.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 \cdot (4 - 1 \cdot 3)$

Step 5

Simplify the answer.

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Step 5.1

Multiply $- 1$ by $3$ .

$4 \cdot (4 - 3)$

Step 5.2

Subtract $3$ from $4$ .

$4 \cdot 1$

Step 5.3

Multiply $4$ by $1$ .

$4$