Calculus Examples

$f (0.5) = \frac{2 x + 4}{\sqrt{x}}$

Step 1

Replace the variable $x$ with $0.5$ in the expression.

$f (0.5) = \frac{2 (0.5) + 4}{\sqrt{0.5}}$

Step 2

Simplify the result.

Tap for more steps...

Step 2.1

Remove parentheses.

$f (0.5) = \frac{2 (0.5) + 4}{\sqrt{0.5}}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $0.5$ .

$f (0.5) = \frac{1 + 4}{\sqrt{0.5}}$

Step 2.2.2

Add $1$ and $4$ .

$f (0.5) = \frac{5}{\sqrt{0.5}}$

Step 2.3

Multiply $\frac{5}{\sqrt{0.5}}$ by $\frac{\sqrt{0.5}}{\sqrt{0.5}}$ .

$f (0.5) = \frac{5}{\sqrt{0.5}} \cdot \frac{\sqrt{0.5}}{\sqrt{0.5}}$

Step 2.4

Combine and simplify the denominator.

Tap for more steps...

Step 2.4.1

Multiply $\frac{5}{\sqrt{0.5}}$ by $\frac{\sqrt{0.5}}{\sqrt{0.5}}$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{\sqrt{0.5} \sqrt{0.5}}$

Step 2.4.2

Raise $\sqrt{0.5}$ to the power of $1$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{\sqrt{0.5} \sqrt{0.5}}$

Step 2.4.3

Raise $\sqrt{0.5}$ to the power of $1$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{\sqrt{0.5} \sqrt{0.5}}$

Step 2.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (0.5) = \frac{5 \sqrt{0.5}}{{\sqrt{0.5}}^{1 + 1}}$

Step 2.4.5

Add $1$ and $1$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{{\sqrt{0.5}}^{2}}$

Step 2.4.6

Rewrite ${\sqrt{0.5}}^{2}$ as $0.5$ .

Tap for more steps...

Step 2.4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.5}$ as ${0.5}^{\frac{1}{2}}$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{{({0.5}^{\frac{1}{2}})}^{2}}$

Step 2.4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{{0.5}^{\frac{1}{2} \cdot 2}}$

Step 2.4.6.3

Combine $\frac{1}{2}$ and $2$ .

$f (0.5) = \frac{5 \sqrt{0.5}}{{0.5}^{\frac{2}{2}}}$

Step 2.4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.6.4.1

Cancel the common factor.

$f (0.5) = \frac{5 \sqrt{0.5}}{{0.5}^{\frac{2}{2}}}$

Step 2.4.6.4.2

Rewrite the expression.

$f (0.5) = \frac{5 \sqrt{0.5}}{0.5}$

Step 2.4.6.5

Evaluate the exponent.

$f (0.5) = \frac{5 \sqrt{0.5}}{0.5}$

Step 2.5

Evaluate the root.

$f (0.5) = \frac{5 \cdot 0.70710678}{0.5}$

Step 2.6

Multiply $5$ by $0.70710678$ .

$f (0.5) = \frac{3.5355339}{0.5}$

Step 2.7

Divide $3.5355339$ by $0.5$ .

$f (0.5) = 7.07106781$

Step 2.8

The final answer is $7.07106781$ .

$7.07106781$

Step 3