Calculus Examples

$f (\frac{π}{4}) = \sec (x)$

Step 1

Replace the variable $x$ with $\frac{π}{4}$ in the expression.

$f (\frac{π}{4}) = \sec (\frac{π}{4})$

Step 2

Simplify the result.

Tap for more steps...

Step 2.1

The exact value of $\sec (\frac{π}{4})$ is $\frac{2}{\sqrt{2}}$ .

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

Step 2.2

Multiply $\frac{2}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$f (\frac{π}{4}) = \frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 2.3

Combine and simplify the denominator.

Tap for more steps...

Step 2.3.1

Multiply $\frac{2}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 2.3.2

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 2.3.3

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 2.3.4

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

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Step 2.3.5

Add $1$ and $1$ .

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{{\sqrt{2}}^{2}}$

Step 2.3.6

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

Tap for more steps...

Step 2.3.6.1

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

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Step 2.3.6.2

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

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Step 2.3.6.3

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

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Step 2.3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.6.4.1

Cancel the common factor.

$f (\frac{π}{4}) = \frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Step 2.3.6.4.2

Rewrite the expression.

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

Step 2.3.6.5

Evaluate the exponent.

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

Step 2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Divide $\sqrt{2}$ by $1$ .

$f (\frac{π}{4}) = \sqrt{2}$

Step 2.5

The final answer is $\sqrt{2}$ .

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Step 4