Calculus Examples

$lim_{x \to π} \frac{π \sin (x)}{x}$

Step 1

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

$π lim_{x \to π} \frac{\sin (x)}{x}$

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

$π \frac{\sin (π)}{lim_{x \to π} x}$

Step 4.2

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

$π \frac{\sin (π)}{π}$

Step 5

Simplify the answer.

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Step 5.1

Cancel the common factor of $π$ .

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Step 5.1.1

Cancel the common factor.

$π \frac{\sin (π)}{π}$

Step 5.1.2

Rewrite the expression.

$\sin (π)$

Step 5.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (0)$

Step 5.3

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

$0$