Calculus Examples

$lim_{x \to 6} x^{\frac{2}{6}}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $2$ and $6$ .

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Step 1.1.1

Factor $2$ out of $2$ .

$lim_{x \to 6} x^{\frac{2 (1)}{6}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $6$ .

$lim_{x \to 6} x^{\frac{2 \cdot 1}{2 \cdot 3}}$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to 6} x^{\frac{2 \cdot 1}{2 \cdot 3}}$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to 6} x^{\frac{1}{3}}$

Step 1.2

Move the exponent $\frac{1}{3}$ from $x^{\frac{1}{3}}$ outside the limit using the Limits Power Rule.

${(lim_{x \to 6} x)}^{\frac{1}{3}}$

Step 2

Evaluate the limit of $x$ by plugging in $6$ for $x$ .

$6^{\frac{1}{3}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6^{\frac{1}{3}}$

Decimal Form:

$1.81712059 \dots$