Calculus Examples

$lim_{x \to 3} \sqrt{2 x - 5}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 3} 2 x - 5}$

Step 1.2

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

$\sqrt{lim_{x \to 3} 2 x - lim_{x \to 3} 5}$

Step 1.3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{2 lim_{x \to 3} x - lim_{x \to 3} 5}$

Step 1.4

Evaluate the limit of $5$ which is constant as $x$ approaches $3$ .

$\sqrt{2 lim_{x \to 3} x - 1 \cdot 5}$

Step 2

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

$\sqrt{2 \cdot 3 - 1 \cdot 5}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $3$ .

$\sqrt{6 - 1 \cdot 5}$

Step 3.2

Multiply $- 1$ by $5$ .

$\sqrt{6 - 5}$

Step 3.3

Subtract $5$ from $6$ .

$\sqrt{1}$

Step 3.4

Any root of $1$ is $1$ .

$1$