Calculus Examples

$\frac{lim_{x \to 0} \tan (- 0.01)}{\tan (4) (- 0.01)}$

Step 1

Evaluate the limit of $\tan (- 0.01)$ which is constant as $x$ approaches $0$ .

$\frac{\tan (- 0.01)}{\tan (4) (- 0.01)}$

Step 2

Simplify the answer.

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Step 2.1

Separate fractions.

$\frac{1}{- 0.01} \cdot \frac{\tan (- 0.01)}{\tan (4)}$

Step 2.2

Rewrite $\tan (4)$ in terms of sines and cosines.

$\frac{1}{- 0.01} \cdot \frac{\tan (- 0.01)}{\frac{\sin (4)}{\cos (4)}}$

Step 2.3

Rewrite $\tan (- 0.01)$ in terms of sines and cosines.

$\frac{1}{- 0.01} \cdot \frac{\frac{\sin (- 0.01)}{\cos (- 0.01)}}{\frac{\sin (4)}{\cos (4)}}$

Step 2.4

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (4)}{\cos (4)}$ .

$\frac{1}{- 0.01} (\frac{\sin (- 0.01)}{\cos (- 0.01)} \cdot \frac{\cos (4)}{\sin (4)})$

Step 2.5

Simplify.

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Step 2.5.1

Convert from $\frac{\sin (- 0.01)}{\cos (- 0.01)}$ to $\tan (- 0.01)$ .

$\frac{1}{- 0.01} (\tan (- 0.01) \frac{\cos (4)}{\sin (4)})$

Step 2.5.2

Convert from $\frac{\cos (4)}{\sin (4)}$ to $\cot (4)$ .

$\frac{1}{- 0.01} (\tan (- 0.01) \cot (4))$

Step 2.6

Divide $1$ by $- 0.01$ .

$- 100 (\tan (- 0.01) \cot (4))$

Step 2.7

Evaluate $\cot (4)$ .

$- 100 (\tan (- 0.01) \cdot 14.30066625)$

Step 2.8

Multiply $\tan (- 0.01)$ by $14.30066625$ .

$- 100 \cdot - 0.00249593$

Step 2.9

Multiply $- 100$ by $- 0.00249593$ .

$0.24959371$