What is the limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x} ?

The limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x} is 1/(sqrt(e))

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limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x}

x \to 0 + lim (\frac{( 1 + x ) ^{\frac{1}{x}}}{e})^{\frac{1}{x}}

\frac{1}{e}

Decimal Notation

0.60653 \dots

Solution steps

x \to 0 + lim (\frac{( 1 + x ) ^{\frac{1}{x}}}{e})^{\frac{1}{x}}

Apply exponent rules

= x \to 0 + lim e^{\frac{1}{x} l n (\frac{( 1 + x ) ^{\frac{1}{x}}}{e})}

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

f (x) = 3 x sin (2 x)

\int \frac{1}{x 6 - x ^{2}} d x

\int sin^{3} (\frac{x}{2}) d x

θ \to \infty lim (e^{- 3 θ} cos (θ))

h \to 0 lim (\frac{( a ^{u + h} - a ^{u} )}{h})

What is the limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x} ?
The limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x} is 1/(sqrt(e))