Calculus Examples

$lim_{x \to \frac{3}{2}} - \sqrt{2 x + 4}$

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 $x$ .

$- lim_{x \to \frac{3}{2}} \sqrt{2 x + 4}$

Step 1.2

Move the limit under the radical sign.

$- \sqrt{lim_{x \to \frac{3}{2}} 2 x + 4}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $\frac{3}{2}$ .

$- \sqrt{lim_{x \to \frac{3}{2}} 2 x + lim_{x \to \frac{3}{2}} 4}$

Step 1.4

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

$- \sqrt{2 lim_{x \to \frac{3}{2}} x + lim_{x \to \frac{3}{2}} 4}$

Step 1.5

Evaluate the limit of $4$ which is constant as $x$ approaches $\frac{3}{2}$ .

$- \sqrt{2 lim_{x \to \frac{3}{2}} x + 4}$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{3}{2}$ for $x$ .

$- \sqrt{2 (\frac{3}{2}) + 4}$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$- \sqrt{2 (\frac{3}{2}) + 4}$

Step 3.1.2

Rewrite the expression.

$- \sqrt{3 + 4}$

Step 3.2

Add $3$ and $4$ .

$- \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{7}$

Decimal Form:

$- 2.64575131 \dots$