Calculus Examples

$\frac{lim_{x \to 0} 8 x}{3 \sin (x)}$

Step 1

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$\frac{8 lim_{x \to 0} x}{3 \sin (x)}$

Step 2

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

$\frac{8 \cdot 0}{3 \sin (x)}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Cancel the common factor of $0$ and $3$ .

Tap for more steps...

Step 3.1.1

Factor $3$ out of $8 \cdot 0$ .

$\frac{3 (8 \cdot 0)}{3 \sin (x)}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $3$ out of $3 \sin (x)$ .

$\frac{3 (8 \cdot 0)}{3 (\sin (x))}$

Step 3.1.2.2

Cancel the common factor.

$\frac{3 (8 \cdot 0)}{3 \sin (x)}$

Step 3.1.2.3

Rewrite the expression.

$\frac{8 \cdot 0}{\sin (x)}$

Step 3.2

Multiply $8$ by $0$ .

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

Step 3.3

Separate fractions.

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

Step 3.4

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{0}{1} \csc (x)$

Step 3.5

Divide $0$ by $1$ .

$0 \csc (x)$

Step 3.6

Multiply $0$ by $\csc (x)$ .

$0$