Calculus Examples

$\frac{lim_{x \to \frac{π}{2}} 6 \cos (x)}{\cot (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{6 lim_{x \to \frac{π}{2}} \cos (x)}{\cot (x)}$

Step 1.2

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

$\frac{6 \cos (lim_{x \to \frac{π}{2}} x)}{\cot (x)}$

Step 2

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

$\frac{6 \cos (\frac{π}{2})}{\cot (x)}$

Step 3

Simplify the answer.

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Step 3.1

Separate fractions.

$\frac{6}{1} \cdot \frac{\cos (\frac{π}{2})}{\cot (x)}$

Step 3.2

Rewrite $\cot (x)$ in terms of sines and cosines.

$\frac{6}{1} \cdot \frac{\cos (\frac{π}{2})}{\frac{\cos (x)}{\sin (x)}}$

Step 3.3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (x)}{\sin (x)}$ .

$\frac{6}{1} (\cos (\frac{π}{2}) \frac{\sin (x)}{\cos (x)})$

Step 3.4

Write $\cos (\frac{π}{2})$ as a fraction with denominator $1$ .

$\frac{6}{1} (\frac{\cos (\frac{π}{2})}{1} \cdot \frac{\sin (x)}{\cos (x)})$

Step 3.5

Simplify.

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Step 3.5.1

Divide $\cos (\frac{π}{2})$ by $1$ .

$\frac{6}{1} (\cos (\frac{π}{2}) \frac{\sin (x)}{\cos (x)})$

Step 3.5.2

Combine $\cos (\frac{π}{2})$ and $\frac{\sin (x)}{\cos (x)}$ .

$\frac{6}{1} \cdot \frac{\cos (\frac{π}{2}) \sin (x)}{\cos (x)}$

Step 3.6

Divide $6$ by $1$ .

$6 \frac{\cos (\frac{π}{2}) \sin (x)}{\cos (x)}$

Step 3.7

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$6 \frac{0 \sin (x)}{\cos (x)}$

Step 3.8

Multiply $0$ by $\sin (x)$ .

$6 \frac{0}{\cos (x)}$

Step 3.9

Divide $0$ by $\cos (x)$ .

$6 \cdot 0$

Step 3.10

Multiply $6$ by $0$ .

$0$