Calculus Examples

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

Step 1

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

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Step 1.1

Evaluate the limit of $\arcsin (x)$ by plugging in $0$ for $x$ .

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

Step 1.2

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

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

Step 2

Simplify the answer.

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Step 2.1

Separate fractions.

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

Step 2.2

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

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

Step 2.3

Divide $0$ by $1$ .

$0 \csc (x)$

Step 2.4

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

$0$