Calculus Examples

$lim_{x \to 2} \sqrt{6 x - 5}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 2} 6 x - 5}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\sqrt{lim_{x \to 2} 6 x - lim_{x \to 2} 5}$

Step 1.3

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{6 lim_{x \to 2} x - lim_{x \to 2} 5}$

Step 1.4

Evaluate the limit of $5$ which is constant as $x$ approaches $2$ .

$\sqrt{6 lim_{x \to 2} x - 1 \cdot 5}$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sqrt{6 \cdot 2 - 1 \cdot 5}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $6$ by $2$ .

$\sqrt{12 - 1 \cdot 5}$

Step 3.2

Multiply $- 1$ by $5$ .

$\sqrt{12 - 5}$

Step 3.3

Subtract $5$ from $12$ .

$\sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7}$

Decimal Form:

$2.64575131 \dots$