What is the limit as x approaches 3 of 1/(x^x) ?

The limit as x approaches 3 of 1/(x^x) is 1/27

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limit as x approaches 3 of 1/(x^x)

x \to 3 lim (\frac{1}{x ^{x}})

\frac{1}{27}

Decimal

0.03703 \dots

Solution steps

x \to 3 lim (\frac{1}{x ^{x}})

Plug in the value

x = 3

= \frac{1}{3 ^{3}}

Simplify

= \frac{1}{27}

x \to 3 lim (6 - 3 x)

x \to 3 lim (\frac{5 + 2}{x})

x \to 3 lim (x^{2} + 3 x - 5)

x \to 3 lim ((\frac{x + 1}{x})^{x})

x \to 3 lim (\frac{( 1 + x ) ^{1}}{x})

What is the limit as x approaches 3 of 1/(x^x) ?
The limit as x approaches 3 of 1/(x^x) is 1/27