Precalculus Examples

lim_{x \to 4} 10 x - 12

$lim_{x \to 4} 10 x - 12$

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

4

$4$ .

lim_{x \to 4} 10 x - lim_{x \to 4} 12

$lim_{x \to 4} 10 x - lim_{x \to 4} 12$

Step 1.2

Move the term

10

$10$ outside of the limit because it is constant with respect to

x

$x$ .

10 lim_{x \to 4} x - lim_{x \to 4} 12

$10 lim_{x \to 4} x - lim_{x \to 4} 12$

Step 1.3

Evaluate the limit of

12

$12$ which is constant as

x

$x$ approaches

4

$4$ .

10 lim_{x \to 4} x - 1 \cdot 12

$10 lim_{x \to 4} x - 1 \cdot 12$

10 lim_{x \to 4} x - 1 \cdot 12

$10 lim_{x \to 4} x - 1 \cdot 12$

Step 2

Evaluate the limit of

x

$x$ by plugging in

4

$4$ for

x

$x$ .

10 \cdot 4 - 1 \cdot 12

$10 \cdot 4 - 1 \cdot 12$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

10

$10$ by

4

$4$ .

40 - 1 \cdot 12

$40 - 1 \cdot 12$

Step 3.1.2

Multiply

- 1

$- 1$ by

12

$12$ .

40 - 12

$40 - 12$

40 - 12

$40 - 12$

Step 3.2

Subtract

12

$12$ from

40

$40$ .

28

$28$

28

$28$

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