What is the limit as x approaches 2 of (1+x)^{1/x} ?

The limit as x approaches 2 of (1+x)^{1/x} is 3^{1/2}

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limit as x approaches 2 of (1+x)^{1/x}

x \to 2 lim ((1 + x)^{\frac{1}{x}})

3^{\frac{1}{2}}

Decimal Notation

1.73205 \dots

Solution steps

x \to 2 lim ((1 + x)^{\frac{1}{x}})

Plug in the value

x = 2

= (1 + 2)^{\frac{1}{2}}

Simplify

= 3^{\frac{1}{2}}

\int \frac{( 1 - x ^{2} )}{x ^{2}} d x

\int - 9 d x

\frac{d}{d x} (\frac{1}{( 3 - x ) ^{4}})

\int t^{3} sin (t) d t

\frac{d y}{d x} + 2 y = e^{2 x} y^{- 2}

What is the limit as x approaches 2 of (1+x)^{1/x} ?
The limit as x approaches 2 of (1+x)^{1/x} is 3^{1/2}