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

The limit as x approaches 3 of ((1+1)/x)^x is 8/27

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

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

\frac{8}{27}

Decimal Notation

0.29629 \dots

Solution steps

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

Plug in the value

x = 3

= (\frac{1 + 1}{3})^{3}

Simplify

(\frac{1 + 1}{3})^{3} : \frac{8}{27}

= \frac{8}{27}

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

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

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

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

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

What is the limit as x approaches 3 of ((1+1)/x)^x ?
The limit as x approaches 3 of ((1+1)/x)^x is 8/27