Calculus Examples

$h (\frac{1}{2}) = t + \frac{7}{t}$

Step 1

Replace the variable $t$ with $\frac{1}{2}$ in the expression.

$h (\frac{1}{2}) = (\frac{1}{2}) + \frac{7}{\frac{1}{2}}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply the numerator by the reciprocal of the denominator.

$h (\frac{1}{2}) = \frac{1}{2} + 7 \cdot 2$

Step 2.1.2

Multiply $7$ by $2$ .

$h (\frac{1}{2}) = \frac{1}{2} + 14$

Step 2.2

To write $14$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$h (\frac{1}{2}) = \frac{1}{2} + 14 \cdot \frac{2}{2}$

Step 2.3

Combine $14$ and $\frac{2}{2}$ .

$h (\frac{1}{2}) = \frac{1}{2} + \frac{14 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$h (\frac{1}{2}) = \frac{1 + 14 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $14$ by $2$ .

$h (\frac{1}{2}) = \frac{1 + 28}{2}$

Step 2.5.2

Add $1$ and $28$ .

$h (\frac{1}{2}) = \frac{29}{2}$

Step 2.6

The final answer is $\frac{29}{2}$ .

$\frac{29}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{2}$

Decimal Form:

$14.5$

Mixed Number Form:

$14 \frac{1}{2}$

Step 4