Precalculus Examples

$lim_{x \to 0} \frac{\sin (2 x)}{2}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{1}{2} lim_{x \to 0} \sin (2 x)$

Step 1.2

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

$\frac{1}{2} \sin (lim_{x \to 0} 2 x)$

Step 1.3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{2} \sin (2 lim_{x \to 0} x)$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{1}{2} \sin (2 \cdot 0)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $0$ .

$\frac{1}{2} \sin (0)$

Step 3.2

The exact value of $\sin (0)$ is $0$ .

$\frac{1}{2} \cdot 0$

Step 3.3

Multiply $\frac{1}{2}$ by $0$ .

$0$