Calculus Examples

$lim_{x \to 2} 12 x - 6$

Evaluate the limit.

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

$lim_{x \to 2} 12 x - lim_{x \to 2} 6$

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$12 lim_{x \to 2} x - lim_{x \to 2} 6$

Evaluate the limit of $6$ which is constant as $x$ approaches $2$ .

$12 lim_{x \to 2} x - 1 \cdot 6$

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

$12 \cdot 2 - 1 \cdot 6$

Simplify the answer.

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Simplify each term.

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Multiply $12$ by $2$ .

$24 - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$24 - 6$

Subtract $6$ from $24$ .

$18$