What is the limit as x approaches 0 of (1+x/3)^{1/x} ?

The limit as x approaches 0 of (1+x/3)^{1/x} is cube root of e

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limit as x approaches 0 of (1+x/3)^{1/x}

x \to 0 lim ((1 + \frac{x}{3})^{\frac{1}{x}})

Decimal Notation

1.39561 \dots

Solution steps

x \to 0 lim ((1 + \frac{x}{3})^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + \frac{x}{3})})

Apply the Limit Chain Rule:

\int (θ^{4} + sec^{2} (θ)) d θ

y = sin (2) (x), y = sin (3) (x), 0 \leq x \leq π

x - \frac{1}{x}

t e^{- t} sin (2 t)

y^{^{'}} - \frac{4}{t} y = t^{5} e^{t}

What is the limit as x approaches 0 of (1+x/3)^{1/x} ?
The limit as x approaches 0 of (1+x/3)^{1/x} is cube root of e