Calculus Examples

$lim_{x \to π} x^{2} - \sin (x)$

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

$lim_{x \to π} x^{2} - lim_{x \to π} \sin (x)$

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

${(lim_{x \to π} x)}^{2} - lim_{x \to π} \sin (x)$

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

${(lim_{x \to π} x)}^{2} - \sin (lim_{x \to π} x)$

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

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

$π^{2} - \sin (lim_{x \to π} x)$

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

$π^{2} - \sin (π)$

Simplify the answer.

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Simplify each term.

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

$π^{2} - \sin (0)$

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

$π^{2} - 0$

Multiply $- 1$ by $0$ .

$π^{2} + 0$

Add $π^{2}$ and $0$ .

$π^{2}$

The result can be shown in multiple forms.

Exact Form:

$π^{2}$

Decimal Form:

$9.86960440 \dots$