Calculus Examples

$lim_{x \to \frac{π}{\frac{}{}} \cdot 2} 9 \sin (x)$

Step 1

Move the term $9$ outside of the limit because it is constant with respect to $x$ .

$9 lim_{x \to \frac{π}{\frac{}{}} \cdot 2} \sin (x)$

Step 2

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

$9 \sin (lim_{x \to \frac{π}{\frac{}{}} \cdot 2} x)$

Step 3

Evaluate the limits by plugging in $\frac{π}{\frac{}{}} \cdot 2$ for all occurrences of $x$ .

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Step 3.1

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

$9 \sin (\frac{π}{\frac{}{}} \cdot 2)$

Step 3.2

Reduce the expression by cancelling the common factors.

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Step 3.2.1

Reduce the expression $\frac{}{}$ by cancelling the common factors.

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Step 3.2.1.1

Cancel the common factor.

$9 \sin (\frac{π}{\frac{}{}} \cdot 2)$

Step 3.2.1.2

Rewrite the expression.

$9 \sin (\frac{π}{\frac{1}{1}} \cdot 2)$

Step 3.2.2

Rewrite the expression.

$9 \sin (\frac{π}{1} \cdot 2)$

Step 3.3

Divide $π$ by $1$ .

$9 \sin (π \cdot 2)$

Step 3.4

Move $2$ to the left of $π$ .

$9 \sin (2 π)$

Step 4

Simplify the answer.

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Step 4.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$9 \sin (0)$

Step 4.2

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

$9 \cdot 0$

Step 4.3

Multiply $9$ by $0$ .

$0$