Calculus Examples

$lim_{x \to π} x + \sin (x)$

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

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

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

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

Simplify terms.

Tap for more steps...

Simplify each term.

Tap for more steps...

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

$π + \sin (lim_{x \to π} x)$

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

$π + \sin (π)$

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

$π + \sin (0)$

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

$π + 0$

Add $π$ and $0$ .

$π$

The result can be shown in multiple forms.

Exact Form:

$π$

Decimal Form:

$3.14159265 \dots$