Calculus Examples

$lim_{x \to 0} \frac{\sin (2 x)}{\cos (2 x)}$

Step 1

Convert from $\frac{\sin (2 x)}{\cos (2 x)}$ to $\tan (2 x)$ .

$lim_{x \to 0} \tan (2 x)$

Step 2

Evaluate the limit.

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Step 2.1

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

$\tan (lim_{x \to 0} 2 x)$

Step 2.2

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

$\tan (2 lim_{x \to 0} x)$

Step 3

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

$\tan (2 \cdot 0)$

Step 4

Simplify the answer.

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Step 4.1

Multiply $2$ by $0$ .

$\tan (0)$

Step 4.2

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

$0$