Precalculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

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

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

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

Step 1.3

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

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

Step 1.4

Evaluate the limit of $2$ which is constant as $x$ approaches $1$ .

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

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\sqrt{3 \cdot 1 - 1 \cdot 2}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $3$ by $1$ .

$\sqrt{3 - 1 \cdot 2}$

Step 3.2

Multiply $- 1$ by $2$ .

$\sqrt{3 - 2}$

Step 3.3

Subtract $2$ from $3$ .

$\sqrt{1}$

Step 3.4

Any root of $1$ is $1$ .

$1$