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

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

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

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

e

Decimal

1.64872 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

- x^{2} + 8 x, x^{2} - 4 x

\frac{d}{d x} (∣ x ∣^{∣ c o s (x) ∣})

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

\int e^{8 t} d t

\frac{\partial}{\partial y} ((x + y) e^{x + 2 y})

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