Precalculus Examples

$\frac{lim_{x \to 0} x^{3}}{\tan (x) - \sin (x)}$

Step 1

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to 0} x)}^{3}}{\tan (x) - \sin (x)}$

Step 2

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

$\frac{0^{3}}{\tan (x) - \sin (x)}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Raising $0$ to any positive power yields $0$ .

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

Step 3.2

Simplify the denominator.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Factor $\sin (x)$ out of $\frac{\sin (x)}{\cos (x)} - \sin (x)$ .

Tap for more steps...

Step 3.2.2.1

Factor $\sin (x)$ out of $\frac{\sin (x)}{\cos (x)}$ .

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

Step 3.2.2.2

Factor $\sin (x)$ out of $- \sin (x)$ .

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

Step 3.2.2.3

Factor $\sin (x)$ out of $\sin (x) \frac{1}{\cos (x)} + \sin (x) \cdot - 1$ .

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

Step 3.3

Divide $0$ by $\sin (x) (\frac{1}{\cos (x)} - 1)$ .

$0$