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

The limit as x approaches 3 of ((x+1)/x)^x is 64/27

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

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

\frac{64}{27}

Decimal Notation

2.37037 \dots

Solution steps

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

Plug in the value

x = 3

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

Simplify

(\frac{3 + 1}{3})^{3} : \frac{64}{27}

= \frac{64}{27}

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

x \to 3 lim (\frac{ln ^{2} ( x )}{x})

x \to 3 lim (x^{2} - 4 x + 1)

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

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

What is the limit as x approaches 3 of ((x+1)/x)^x ?
The limit as x approaches 3 of ((x+1)/x)^x is 64/27