Precalculus Examples

$lim_{x \to 3} 3 x - 2$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$lim_{x \to 3} 3 x - lim_{x \to 3} 2$

Step 1.2

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 3} x - lim_{x \to 3} 2$

Step 1.3

Evaluate the limit of $2$ which is constant as $x$ approaches $3$ .

$3 lim_{x \to 3} x - 1 \cdot 2$

Step 2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$3 \cdot 3 - 1 \cdot 2$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $3$ by $3$ .

$9 - 1 \cdot 2$

Step 3.1.2

Multiply $- 1$ by $2$ .

$9 - 2$

Step 3.2

Subtract $2$ from $9$ .

$7$