Calculus Examples

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

Step 1

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

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

Step 2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3$ .

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

Step 3

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

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

Step 4

Evaluate the limits by plugging in $3$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

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

Step 4.2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$3 \frac{\sin (3)}{3}$

Step 5

Simplify the answer.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Cancel the common factor.

$3 \frac{\sin (3)}{3}$

Step 5.1.2

Rewrite the expression.

$\sin (3)$

Step 5.2

Evaluate $\sin (3)$ .

$0.05233595$