Calculus Examples

$\frac{lim_{x \to 6 π} \sin^{2} (x)}{x - 6 x}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the exponent $2$ from $\sin^{2} (x)$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to 6 π} \sin (x))}^{2}}{x - 6 x}$

Step 1.2

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

$\frac{\sin^{2} (lim_{x \to 6 π} x)}{x - 6 x}$

Step 2

Evaluate the limit of $x$ by plugging in $6 π$ for $x$ .

$\frac{\sin^{2} (6 π)}{x - 6 x}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

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

$\frac{\sin^{2} (0)}{x - 6 x}$

Step 3.1.2

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

$\frac{0^{2}}{x - 6 x}$

Step 3.1.3

Raising $0$ to any positive power yields $0$ .

$\frac{0}{x - 6 x}$

Step 3.2

Subtract $6 x$ from $x$ .

$\frac{0}{- 5 x}$

Step 3.3

Cancel the common factor of $0$ and $- 5$ .

Tap for more steps...

Step 3.3.1

Factor $5$ out of $0$ .

$\frac{5 (0)}{- 5 x}$

Step 3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.1

Factor $5$ out of $- 5 x$ .

$\frac{5 (0)}{5 (- x)}$

Step 3.3.2.2

Cancel the common factor.

$\frac{5 \cdot 0}{5 (- x)}$

Step 3.3.2.3

Rewrite the expression.

$\frac{0}{- x}$

Step 3.4

Divide $0$ by $- x$ .

$0$