Calculus Examples

$\frac{lim_{x \to 0} 14 \arctan (x)}{8 x}$

Step 1

Move the term $14$ outside of the limit because it is constant with respect to $x$ .

$\frac{14 lim_{x \to 0} \arctan (x)}{8 x}$

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 $\arctan (x)$ by plugging in $0$ for $x$ .

$\frac{14 \arctan (0)}{8 x}$

Step 2.2

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

$\frac{14 \cdot 0}{8 x}$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $14$ and $8$ .

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Step 3.1.1

Factor $2$ out of $14 \cdot 0$ .

$\frac{2 (7 \cdot 0)}{8 x}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $8 x$ .

$\frac{2 (7 \cdot 0)}{2 (4 x)}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (7 \cdot 0)}{2 (4 x)}$

Step 3.1.2.3

Rewrite the expression.

$\frac{7 \cdot 0}{4 x}$

Step 3.2

Cancel the common factor of $0$ and $4$ .

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Step 3.2.1

Factor $4$ out of $7 \cdot 0$ .

$\frac{4 (7 \cdot 0)}{4 x}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $4$ out of $4 x$ .

$\frac{4 (7 \cdot 0)}{4 (x)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{4 (7 \cdot 0)}{4 x}$

Step 3.2.2.3

Rewrite the expression.

$\frac{7 \cdot 0}{x}$

Step 3.3

Multiply $7$ by $0$ .

$\frac{0}{x}$

Step 3.4

Divide $0$ by $x$ .

$0$