Calculus Examples

$\frac{lim_{x \to 0} (\cos (x)) \tan (x)}{x}$

Step 1

Apply trigonometric identities.

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Step 1.1

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

$\frac{lim_{x \to 0} \cos (x) \frac{\sin (x)}{\cos (x)}}{x}$

Step 1.2

Cancel the common factor of $\cos (x)$ .

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Step 1.2.1

Cancel the common factor.

$\frac{lim_{x \to 0} \cos (x) \frac{\sin (x)}{\cos (x)}}{x}$

Step 1.2.2

Rewrite the expression.

$\frac{lim_{x \to 0} \sin (x)}{x}$

Step 2

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

$\frac{\sin (lim_{x \to 0} x)}{x}$

Step 3

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

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

Step 4

Simplify the answer.

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Step 4.1

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

$\frac{0}{x}$

Step 4.2

Divide $0$ by $x$ .

$0$