Calculus Examples

$lim_{x \to π} 12 \sin (\frac{x}{6})$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$12 lim_{x \to π} \sin (\frac{x}{6})$

Step 1.2

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

$12 \sin (lim_{x \to π} \frac{x}{6})$

Step 1.3

Move the term $\frac{1}{6}$ outside of the limit because it is constant with respect to $x$ .

$12 \sin (\frac{1}{6} lim_{x \to π} x)$

Step 2

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

$12 \sin (\frac{1}{6} π)$

Step 3

Simplify the answer.

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Step 3.1

Combine $\frac{1}{6}$ and $π$ .

$12 \sin (\frac{π}{6})$

Step 3.2

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

$12 (\frac{1}{2})$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $12$ .

$2 (6) \frac{1}{2}$

Step 3.3.2

Cancel the common factor.

$2 \cdot 6 \frac{1}{2}$

Step 3.3.3

Rewrite the expression.

$6$