Calculus Examples

$\frac{lim_{x \to 0} 6 \sin (x)}{7 x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{6 lim_{x \to 0} \sin (x)}{7 x}$

Step 1.2

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

$\frac{6 \sin (lim_{x \to 0} x)}{7 x}$

Step 2

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

$\frac{6 \sin (0)}{7 x}$

Step 3

Simplify the answer.

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Step 3.1

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

$\frac{6 \cdot 0}{7 x}$

Step 3.2

Multiply $6$ by $0$ .

$\frac{0}{7 x}$

Step 3.3

Cancel the common factor of $0$ and $7$ .

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Step 3.3.1

Factor $7$ out of $0$ .

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $7$ out of $7 x$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

$\frac{0}{x}$

Step 3.4

Divide $0$ by $x$ .

$0$