Calculus Examples

$\frac{lim_{x \to 0} x^{2}}{\sin^{2} (3 x)}$

Step 1

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to 0} x)}^{2}}{\sin^{2} (3 x)}$

Step 2

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

$\frac{0^{2}}{\sin^{2} (3 x)}$

Step 3

Simplify the answer.

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Step 3.1

Multiply by $1$ .

$\frac{0^{2}}{\sin^{2} (3 x) \cdot 1}$

Step 3.2

Separate fractions.

$\frac{0^{2}}{1} \cdot \frac{1}{\sin^{2} (3 x)}$

Step 3.3

Convert from $\frac{1}{\sin^{2} (3 x)}$ to $\csc^{2} (3 x)$ .

$\frac{0^{2}}{1} \csc^{2} (3 x)$

Step 3.4

Divide $0^{2}$ by $1$ .

$0^{2} \csc^{2} (3 x)$

Step 3.5

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

$0 \csc^{2} (3 x)$

Step 3.6

Multiply $0$ by $\csc^{2} (3 x)$ .

$0$