Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.2

Move the limit under the radical sign.

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $2$ .

$- \sqrt{4 + 1}$

Step 3.2

Add $4$ and $1$ .

$- \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{5}$

Decimal Form:

$- 2.23606797 \dots$