Calculus Examples

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

Step 1

Move the term $\sin (3)$ outside of the limit because it is constant with respect to $x$ .

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

Step 2

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

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

Step 3

Simplify the answer.

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Separate fractions.

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

Rewrite $\frac{\sin (3)}{\sin (2)}$ as a product.

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

Write $\sin (3)$ as a fraction with denominator $1$ .

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

Simplify.

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Divide $\sin (3)$ by $1$ .

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

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

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

Divide $0$ by $x$ .

$0 (\sin (3) \csc (2))$

Evaluate $\sin (3)$ .

$0 (0.05233595 \csc (2))$

Evaluate $\csc (2)$ .

$0 (0.05233595 \cdot 28.65370834)$

Multiply $0 (0.05233595 \cdot 28.65370834)$ .

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Multiply $0.05233595$ by $28.65370834$ .

$0 \cdot 1.49961922$

Multiply $0$ by $1.49961922$ .

$0$