Calculus Examples

$lim_{x \to \frac{π}{3}} \sin (\frac{x}{2})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\sin (lim_{x \to \frac{π}{3}} \frac{x}{2})$

Step 1.2

Move the term $\frac{1}{2}$ outside of the limit because it is constant with respect to $x$ .

$\sin (\frac{1}{2} lim_{x \to \frac{π}{3}} x)$

Step 2

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

$\sin (\frac{1}{2} \cdot \frac{π}{3})$

Step 3

Simplify the answer.

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Step 3.1

Multiply $\frac{1}{2} \cdot \frac{π}{3}$ .

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Step 3.1.1

Multiply $\frac{1}{2}$ by $\frac{π}{3}$ .

$\sin (\frac{π}{2 \cdot 3})$

Step 3.1.2

Multiply $2$ by $3$ .

$\sin (\frac{π}{6})$

Step 3.2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$