Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the term $- 3$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.2

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

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

Step 1.3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

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

Step 2

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

$- 3 \sin (3 \frac{π}{2})$

Step 3

Simplify the answer.

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Step 3.1

Combine $3$ and $\frac{π}{2}$ .

$- 3 \sin (\frac{3 π}{2})$

Step 3.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$- 3 (- \sin (\frac{π}{2}))$

Step 3.3

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

$- 3 (- 1 \cdot 1)$

Step 3.4

Multiply $- 3 (- 1 \cdot 1)$ .

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Step 3.4.1

Multiply $- 1$ by $1$ .

$- 3 \cdot - 1$

Step 3.4.2

Multiply $- 3$ by $- 1$ .

$3$