Calculus Examples

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

Step 1

Move the limit inside the trig function because sine is continuous.

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

Step 2

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

$\frac{\sin (0)}{5 x}$

Step 3

Simplify the answer.

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Step 3.1

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

$\frac{0}{5 x}$

Step 3.2

Cancel the common factor of $0$ and $5$ .

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Step 3.2.1

Factor $5$ out of $0$ .

$\frac{5 (0)}{5 x}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $5$ out of $5 x$ .

$\frac{5 (0)}{5 (x)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{5 \cdot 0}{5 x}$

Step 3.2.2.3

Rewrite the expression.

$\frac{0}{x}$

Step 3.3

Divide $0$ by $x$ .

$0$