Calculus Examples

$lim_{x \to π} | \sin (x) |$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the absolute value signs.

$| lim_{x \to π} \sin (x) |$

Step 1.2

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

$| \sin (lim_{x \to π} x) |$

Step 2

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

$| \sin (π) |$

Step 3

Simplify the answer.

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Step 3.1

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

$| \sin (0) |$

Step 3.2

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

$| 0 |$

Step 3.3

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$0$