Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

$\frac{\tan (0 + 0)}{x - \sin (x)}$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Add $0$ and $0$ .

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

Step 4.1.2

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

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

Step 4.2

Divide $0$ by $x - \sin (x)$ .

$0$