Calculus Examples

$lim_{x \to 8} x \cot (2 x)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $8$ .

$lim_{x \to 8} x \cdot lim_{x \to 8} \cot (2 x)$

Step 2

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

$lim_{x \to 8} x \cdot \cot (lim_{x \to 8} 2 x)$

Step 3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$lim_{x \to 8} x \cdot \cot (2 lim_{x \to 8} x)$

Step 4

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$8 \cdot \cot (2 lim_{x \to 8} x)$

Step 4.2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$8 \cdot \cot (2 \cdot 8)$

Step 5

Simplify the answer.

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Step 5.1

Multiply $2$ by $8$ .

$8 \cdot \cot (16)$

Step 5.2

Evaluate $\cot (16)$ .

$8 \cdot 3.48741444$

Step 5.3

Multiply $8$ by $3.48741444$ .

$27.89931555$