Calculus Examples

$\frac{lim_{x \to 0} x \tan (x)}{1 - \cos (x)}$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} x \cdot lim_{x \to 0} \tan (x)}{1 - \cos (x)}$

Step 2

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

$\frac{lim_{x \to 0} x \cdot \tan (lim_{x \to 0} x)}{1 - \cos (x)}$

Step 3

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 3.1

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

$\frac{0 \cdot \tan (lim_{x \to 0} x)}{1 - \cos (x)}$

Step 3.2

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

$\frac{0 \cdot \tan (0)}{1 - \cos (x)}$

Step 4

Simplify the answer.

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Step 4.1

Multiply $0$ by $\tan (0)$ .

$\frac{0}{1 - \cos (x)}$

Step 4.2

Divide $0$ by $1 - \cos (x)$ .

$0$