Calculus Examples

$lim_{x \to 0} 5 x - 4$

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 $0$ .

$lim_{x \to 0} 5 x - lim_{x \to 0} 4$

Step 1.2

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$5 lim_{x \to 0} x - lim_{x \to 0} 4$

Step 1.3

Evaluate the limit of $4$ which is constant as $x$ approaches $0$ .

$5 lim_{x \to 0} x - 1 \cdot 4$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$5 \cdot 0 - 1 \cdot 4$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $5$ by $0$ .

$0 - 1 \cdot 4$

Step 3.1.2

Multiply $- 1$ by $4$ .

$0 - 4$

Step 3.2

Subtract $4$ from $0$ .

$- 4$