Calculus Examples

$lim_{x \to 0} \sin^{2} (x)$

Step 1

Evaluate the limit.

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Step 1.1

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

${(lim_{x \to 0} \sin (x))}^{2}$

Step 1.2

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

$\sin^{2} (lim_{x \to 0} x)$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\sin^{2} (0)$

Step 3

Simplify the answer.

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Step 3.1

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

$0^{2}$

Step 3.2

Raising $0$ to any positive power yields $0$ .

$0$