Calculus Examples

$lim_{x \to \frac{π}{12}} \tan (36 (x))$

Step 1

Evaluate the limit.

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Step 1.1

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

$\tan (lim_{x \to \frac{π}{12}} 36 (x))$

Step 1.2

Move the term $36$ outside of the limit because it is constant with respect to $x$ .

$\tan (36 lim_{x \to \frac{π}{12}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{π}{12}$ for $x$ .

$\tan (36 \frac{π}{12})$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $12$ .

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Step 3.1.1

Factor $12$ out of $36$ .

$\tan (12 (3) \frac{π}{12})$

Step 3.1.2

Cancel the common factor.

$\tan (12 \cdot 3 \frac{π}{12})$

Step 3.1.3

Rewrite the expression.

$\tan (3 π)$

Step 3.2

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

$\tan (π)$

Step 3.3

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

$- \tan (0)$

Step 3.4

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

$- 0$

Step 3.5

Multiply $- 1$ by $0$ .

$0$