Calculus Examples

$lim_{x \to 4} 3 x (x + 5)$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 4} x (x + 5)$

Step 2

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

$3 lim_{x \to 4} x \cdot lim_{x \to 4} x + 5$

Step 3

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

$3 lim_{x \to 4} x \cdot (lim_{x \to 4} x + lim_{x \to 4} 5)$

Step 4

Evaluate the limit of $5$ which is constant as $x$ approaches $4$ .

$3 lim_{x \to 4} x \cdot (lim_{x \to 4} x + 5)$

Step 5

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

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Step 5.1

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

$3 \cdot 4 \cdot (lim_{x \to 4} x + 5)$

Step 5.2

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

$3 \cdot 4 \cdot (4 + 5)$

Step 6

Simplify the answer.

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Step 6.1

Multiply $3$ by $4$ .

$12 \cdot (4 + 5)$

Step 6.2

Add $4$ and $5$ .

$12 \cdot 9$

Step 6.3

Multiply $12$ by $9$ .

$108$