Calculus Examples

$\frac{lim_{x \to 8} \sin (3 x)}{13 x}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{\sin (lim_{x \to 8} 3 x)}{13 x}$

Step 1.2

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{\sin (3 lim_{x \to 8} x)}{13 x}$

Step 2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{\sin (3 \cdot 8)}{13 x}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $3$ by $8$ .

$\frac{\sin (24)}{13 x}$

Step 3.1.2

Evaluate $\sin (24)$ .

$\frac{0.40673664}{13 x}$

Step 3.2

Factor $0.40673664$ out of $0.40673664$ .

$\frac{0.40673664 (1)}{13 x}$

Step 3.3

Factor $13$ out of $13 x$ .

$\frac{0.40673664 (1)}{13 (x)}$

Step 3.4

Separate fractions.

$\frac{0.40673664}{13} \cdot \frac{1}{x}$

Step 3.5

Divide $0.40673664$ by $13$ .

$0.03128743 \frac{1}{x}$

Step 3.6

Combine $0.03128743$ and $\frac{1}{x}$ .

$\frac{0.03128743}{x}$