What is the limit as x approaches 0 of (1+x/2)^{3/x} ?

The limit as x approaches 0 of (1+x/2)^{3/x} is e^{3/2}

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limit as x approaches 0 of (1+x/2)^{3/x}

x \to 0 lim ((1 + \frac{x}{2})^{\frac{3}{x}})

e^{\frac{3}{2}}

Decimal Notation

4.48168 \dots

Solution steps

x \to 0 lim ((1 + \frac{x}{2})^{\frac{3}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (1 + \frac{x}{2})})

Apply the Limit Chain Rule:

e^{\frac{3}{2}}

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

\frac{d}{d x} (ln (x^{2} - 4 x + 5))

x_{1} + x_{2} + x_{3} - 12

\int e^{- x} cos (8 x) d x

\frac{\partial}{\partial x} (12 x^{4} - 6 x^{2} y + 4 y^{3})

\frac{d}{d x} (x^{\frac{3}{5}} (4 - x))

What is the limit as x approaches 0 of (1+x/2)^{3/x} ?
The limit as x approaches 0 of (1+x/2)^{3/x} is e^{3/2}