Calculus Examples

$\frac{lim_{x \to 0} \sqrt{x^{2}}}{x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\frac{\sqrt{lim_{x \to 0} x^{2}}}{x}$

Step 1.2

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

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

Step 2

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

$\frac{\sqrt{0^{2}}}{x}$

Step 3

Simplify the answer.

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Step 3.1

Pull terms out from under the radical, assuming positive real numbers.

$\frac{0}{x}$

Step 3.2

Divide $0$ by $x$ .

$0$