Calculus Examples

lim_{x \to 2} 12 x - 6

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

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as

x

$x$ approaches

2

$2$ .

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

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

Step 1.2

Move the term

12

$12$ outside of the limit because it is constant with respect to

x

$x$ .

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

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

Step 1.3

Evaluate the limit of

6

$6$ which is constant as

x

$x$ approaches

2

$2$ .

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

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

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

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

Step 2

Evaluate the limit of

x

$x$ by plugging in

2

$2$ for

x

$x$ .

12 \cdot 2 - 1 \cdot 6

$12 \cdot 2 - 1 \cdot 6$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

12

$12$ by

2

$2$ .

24 - 1 \cdot 6

$24 - 1 \cdot 6$

Step 3.1.2

Multiply

- 1

$- 1$ by

6

$6$ .

24 - 6

$24 - 6$

24 - 6

$24 - 6$

Step 3.2

Subtract

6

$6$ from

24

$24$ .

18

$18$

18

$18$

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