Calculus Examples

$lim_{x \to \frac{π}{2}} \frac{\cos (\frac{π}{8} x) π}{8}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the term $\frac{π}{8}$ outside of the limit because it is constant with respect to $x$ .

$\frac{π}{8} lim_{x \to \frac{π}{2}} \cos (\frac{π}{8} x)$

Step 1.2

Move the limit inside the trig function because cosine is continuous.

$\frac{π}{8} \cos (lim_{x \to \frac{π}{2}} \frac{π}{8} x)$

Step 1.3

Move the term $\frac{π}{8}$ outside of the limit because it is constant with respect to $x$ .

$\frac{π}{8} \cos (\frac{π}{8} lim_{x \to \frac{π}{2}} x)$

Step 2

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

$\frac{π}{8} \cos (\frac{π}{8} \cdot \frac{π}{2})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Multiply $\frac{π}{8} \cdot \frac{π}{2}$ .

Tap for more steps...

Step 3.1.1

Multiply $\frac{π}{8}$ by $\frac{π}{2}$ .

$\frac{π}{8} \cos (\frac{π π}{8 \cdot 2})$

Step 3.1.2

Raise $π$ to the power of $1$ .

$\frac{π}{8} \cos (\frac{π^{1} π}{8 \cdot 2})$

Step 3.1.3

Raise $π$ to the power of $1$ .

$\frac{π}{8} \cos (\frac{π^{1} π^{1}}{8 \cdot 2})$

Step 3.1.4

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

$\frac{π}{8} \cos (\frac{π^{1 + 1}}{8 \cdot 2})$

Step 3.1.5

Add $1$ and $1$ .

$\frac{π}{8} \cos (\frac{π^{2}}{8 \cdot 2})$

Step 3.1.6

Multiply $8$ by $2$ .

$\frac{π}{8} \cos (\frac{π^{2}}{16})$

Step 3.2

Evaluate $\cos (\frac{π^{2}}{16})$ .

$\frac{π}{8} \cdot 0.81570451$

Step 3.3

Multiply $\frac{π}{8} \cdot 0.81570451$ .

Tap for more steps...

Step 3.3.1

Combine $\frac{π}{8}$ and $0.81570451$ .

$\frac{π \cdot 0.81570451}{8}$

Step 3.3.2

Multiply $π$ by $0.81570451$ .

$\frac{2.56261131}{8}$

Step 3.4

Divide $2.56261131$ by $8$ .

$0.32032641$