Calculus Examples

$lim_{x \to 6} \cot (\frac{x π}{8})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cot (lim_{x \to 6} \frac{x π}{8})$

Step 1.2

Move the term $\frac{π}{8}$ outside of the limit because it is constant with respect to $x$ .

$\cot (\frac{π}{8} lim_{x \to 6} x)$

Step 2

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

$\cot (\frac{π}{8} \cdot 6)$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $8$ .

$\cot (\frac{π}{2 (4)} \cdot 6)$

Step 3.1.2

Factor $2$ out of $6$ .

$\cot (\frac{π}{2 \cdot 4} \cdot (2 \cdot 3))$

Step 3.1.3

Cancel the common factor.

$\cot (\frac{π}{2 \cdot 4} \cdot (2 \cdot 3))$

Step 3.1.4

Rewrite the expression.

$\cot (\frac{π}{4} \cdot 3)$

Step 3.2

Combine $\frac{π}{4}$ and $3$ .

$\cot (\frac{π \cdot 3}{4})$

Step 3.3

Move $3$ to the left of $π$ .

$\cot (\frac{3 \cdot π}{4})$

Step 3.4

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

$- \cot (\frac{π}{4})$

Step 3.5

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$- 1 \cdot 1$

Step 3.6

Multiply $- 1$ by $1$ .

$- 1$