Calculus Examples

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

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 $x$ approaches $4$ .

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

Step 1.2

Move the term $10$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.3

Evaluate the limit of $12$ which is constant as $x$ approaches $4$ .

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

Step 2

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

$10 \cdot 4 - 1 \cdot 12$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $10$ by $4$ .

$40 - 1 \cdot 12$

Step 3.1.2

Multiply $- 1$ by $12$ .

$40 - 12$

Step 3.2

Subtract $12$ from $40$ .

$28$

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