Calculus Examples

$lim_{x \to 0} \frac{\arcsin (4 x)}{\arccos (5 x)}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} \arcsin (4 x)}{lim_{x \to 0} \arccos (5 x)}$

Step 2

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

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Step 2.1

Evaluate the limit of $\arcsin (4 x)$ by plugging in $0$ for $x$ .

$\frac{\arcsin (4 \cdot 0)}{lim_{x \to 0} \arccos (5 x)}$

Step 2.2

Multiply $4$ by $0$ .

$\frac{\arcsin (0)}{lim_{x \to 0} \arccos (5 x)}$

Step 2.3

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

$\frac{0}{lim_{x \to 0} \arccos (5 x)}$

Step 2.4

Evaluate the limit of $\arccos (5 x)$ by plugging in $0$ for $x$ .

$\frac{0}{\arccos (5 \cdot 0)}$

Step 2.5

Multiply $5$ by $0$ .

$\frac{0}{\arccos (0)}$

Step 2.6

The exact value of $\arccos (0)$ is $\frac{π}{2}$ .

$\frac{0}{\frac{π}{2}}$

Step 3

Simplify the answer.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$0 \frac{2}{π}$

Step 3.2

Multiply $0$ by $\frac{2}{π}$ .

$0$