Calculus Examples

$lim_{x \to 2} \sin (\frac{π x}{2})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\sin (lim_{x \to 2} \frac{π x}{2})$

Step 1.2

Move the term $\frac{π}{2}$ outside of the limit because it is constant with respect to $x$ .

$\sin (\frac{π}{2} lim_{x \to 2} x)$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sin (\frac{π}{2} \cdot 2)$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$\sin (\frac{π}{2} \cdot 2)$

Step 3.1.2

Rewrite the expression.

$\sin (π)$

Step 3.2

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

$\sin (0)$

Step 3.3

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

$0$